Q: Find the critical points of the function f(x)=x4−5x4+5x3−1.
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Q: The population of a city is expected to be P(x) = x(x2 + 36)−1/2 million people after x years. Find…
A: Given, The population of a city is expected to be Px=xx2+36-12 million people after x years.…
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Q: 4. Find all relative maxima, relative minima, and saddle points for the function: f(x.y)= 2x³ + xy²…
A: Given: The function, fx,y=2x3+xy2+5x2+y2.
Q: Find the locations and values of all relative maxima and minima. f(x)=ln(3x)/2x^2
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Q: Please I want solution of question 4 with step by step. Many Thanks
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Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3
A: f(x) is continuous at x = k if
Q: b) Find the absolute maximum and minimum values of function f(x) = (x– 2)5 over the interval [-3, 4]
A: Absolute extrema can occur either at the points of local extrema or the boundaries of the interval.…
Q: 2 The function f(x) is linear and it decreases for all values of x. On the coordinate plane, draw a…
A: We want to find a decreasing linear function.
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A: we have to find value of a and b so function to be continous
Q: 2 Z= 22,
A: Given z=2x12+x1x2+4x22+x1x3+x32+2
Q: Find the critical values of the function below. **x-24x? 8 -x³–24x² f(x)
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Q: Does y = e- - 2 exist? What is the domain & range of the function if it does exist?
A: NOTE: According to guideline answer of first question can be given, for other please ask in a…
Q: Differentiate. f(x) = - 2 e -X t'(x) = ]
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Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.
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Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x + 2 and g(x) х — 2 are the…
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Q: 4) f(x): g(x) = - 3x
A: Given, f(x)=1x and transform the graph into g(x)=-13x
Q: 4. Determine the value of the constant k so that f(x) = e* (x + k) decreases on the intervals (- 0,…
A: we have to find value of k
Q: The population of a city is expected to be P(x) = x(x2 + 36)−1/2 million people after x years. Find…
A: Given function is The average value of population between year x = 0 and year x = 8 is
Q: Determine the extreme values of the ff. functions. f(x) = x^2 + 3 on [1,3]
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Q: F(x)= X^3-18X^2+81X Maximas occur at x=
A: Assume x=c is the critical point of f(x). If f'(x)>0 to the left of x=c and f'(x)<0 to the…
Q: g(x) = \f(x)| h(x) - f(lx|)
A: -4,2,-3,2,-2,0,-1,-2,0,-1,1,-2,2,-0.5,3,0.8 and 4,2 The above coordinates are lies on the graph of…
Q: Find all relative extrema of the function ƒ (x) = 2x° – 6x + 1 %3D
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Q: Find the critical points and determine whether they are minima, maxima, or neither: f (x) = x2/3(1 −…
A: Given: fx=x231-x
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A: To find maximum or minimum of a function, we will take first derivative of f(x) to find critical…
Q: The function f(x) = 2x³ – 21x² + 60x – 7 has two critical values. The smaller one equals and the…
A: The given function is f(x)=2x3-21x2+60x-7
Q: 5. Find all relative maxima of the given function. y =x* -8x' +16x² +3
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Q: Find the extreme values of the function f(x) = x3 + 9x² + 5 on the interval x E [-1,3]
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Q: f(x) = (x-1)(x-6) g (x) =x+4
A: Given, fx=x-1x-6 , gx=x+4
Q: Solve the Problem. Approximate the curve of the given function f. f(x) = x³ + 2x2 – 15x
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Q: f(x) = is the range in which the function is decreasing.
A: fx=exx Differentiating with respect to x, we get f'x=dexdx·x-dxdx·exx2…
Q: The population of a city is expected to be P(x) = x(x2 + 64)−1/2 million people after x years. Find…
A: We will use the average of a function formula
Q: Find the locations and values of all relative maxima and minima ƒ(x) = x + 1/x
A: Given: fx=x+1x We know that for any given functionfx, relative maxima occurs at a value of x where…
Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*
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Q: find the value of the constant (a, b, or c) that makes the function continuous
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Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x+ 2 and g(x) х— 2 are the same…
A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…
Q: Consider the function f(x) = 2x interval - 2, 2|. Find the average or mean slope of the function on…
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Q: (A) Find the absolute maxima and minima for x3 y = - x + 5 over 3 [-V2, v2]. (B) Use the second…
A: When on critical point f''<0 then that critical point give local maximum value of f(x) When on…
Q: Find the absolute extreme values of the function on the interval. f(x)=ln(x+2)+1/x , 1 less than or…
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Q: Find all relative extrema of F(x)= Ln(x^3+3x^2+2)
A: Given, f(x) = ln(x3 +3x2 +2 ) Differentiating the f(x) with respect to x f'(x) = 3x2 +6x +0x3 +3x2…
Q: The derivative of a function is g'(x) = 19 – 6x² and the graph of g(x) passes through the point P(3,…
A: To find g(x)
Q: Find the average rate of change of the function from x1 to x2. Function x-Values f(x) = -3x3 + 3x? +…
A: Recall: Average Rate of Change of a Function : Ax=f(b)-f(a)b-a; where , f(a) and f(b) are the…
Q: Find the value of constant K that makes the function below continuous at x = 4. x2 - 4x X< 4 f(x) =…
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Q: Find the absolute maximum value of the function. f(x) = 2(x – e*)
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Q: Find the locations and values of all relative maxima and minima. f(x)=xe^x/x-1
A: By using double derivative test we can find maxima and minima of the function
Q: This extreme value problem has a extreme values of the function sub f(x, y) = 4x + 8y, x2 maximum…
A: Method of Lagrange's multiplier: The Lagrange multiplier method is a straightforward and elegant way…
Q: h(x) = 6x2; f · g {f(x), g(x)} =
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Q: 2) f(x) = x + 5 glx) = -x - 5x Find f(g(-4))
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Q: 6. What is a point of inflexion ? Does f(x) = x' have a point of inflexion at x = 0?
A: Given that,
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- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.Find the critical points and determine if the function is increasing or decreasing at the given intervals. y=9x^4+2x^3 Left critical point: c1= ?????????Right critical point: c2= ??????? The function is:decrease or increase on (−∞,c1).decrease or increase on (c1,c2).decrease or increase on (c2,∞).Find the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x) = 2x3 − 24x + 8 Step 1 Recall that a critical point is any interior point x in the domain of f where f '(x) = 0 or f '(x) is not defined. To find the critical points of g(x), first find the first derivative g'(x). Since g(x) = 2x3 − 24x + 8, then g'(x) = x2 − 24.
- Determine the smallest value of the constant a for which the graph of the function f(x) = ax−x is always above the x−axis. Help me fast so that I will give good rating.4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer.B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.C. Find the value of f(-1).A problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.
- Find the critical points and determine if the function is increasing or decreasing on the given intervals. y=9x^4+2x^3 Left critical point: c1= Right critical point: c2= The function is: increasing or decreasing (−∞,c1)??????? increasing or decreasing (c1,c2) ?????increasing or decreasing (c2,∞)???????Life Span On the basis of data and projections for theyears 1910 through 2020 the expected life span ofpeople in the United States can be described by thefunction f (x) = 11.027 + 14.304 ln x years, wherex is the number of years from 1900 to the person’sbirth year.a. What does this model estimate the life span to befor people born in 1925? In 2007? (Give eachanswer to the nearest year.)b. Explain why these numbers are so different.In a table, analyze the critical points of the following function ( and from the data collected from the table draw the graph). Find attached an example of the table to be used to analyze the given function. x CRITICAL VALUES f'(x) f(x) f''(x)
- A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of 0.05 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 L/s. The mixture is kept stirred and is pumped out at a rate of 10 L/s. Find the amount of chlorine in the tank as a function of time. (Let y be the amount of chlorine in grams and t be the time in seconds.)An investor has his savings invested in various investments. The amount at the end of each month, in the first semester, is shown in the table. a. Assuming that the rate of change of the amount can be represented by: y ′ (x) = (0.06y (x)) / x, obtain an approximation for the amount in the month of August, using the Improved Euler method, using h = 1 and initial condition given by the data for the month of June.b. What is the relative percentage error knowing that the particular solution of the PVI is y (x) = e ^ (0.06 lnx + 4.46).The relation between the magnitude of a sensation y and the magnitude of the stimulus x is given by y = k(x − x0)n where k is a constant, x0 is the threshold of effective stimulus, and n depends on the type of stimulus. Find the rate of change of sensation with respect to the amount of stimulus given. For electrical stimulation y = k(x − x0)7/2 y' =