Find (algebraically) the absolute maximum and minimum values of f(x) = (x^2) / (x - 1) on (1, 4), if any, and state where those values occur. If f has no absolute maximum or minimum value, explain why.

Q: Find the critical points, domain endpoints, and local extreme values for the function. y = 4x/16 -…

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Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

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Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Let f(x)= x2 -3x + In x. Find the local maximum and minimum values of f by using the second…

A: Since, we are given f(x)=x2-3x+ln x and our aim is to find the local maximum and minimum values of f…

Q: Find any local maximum & local minimum  of f(x)=-0.4x3-0.6x2+3x-4 on the interval (-6,4)

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Q: Find the quadratic approximation to f(x) = /x + 3 near a = 1. Graph f, the quadratic approximation,…

A: fx=x+3

Q: Describe the procedure for finding critical points of a function in two independent variables

A: Based on the theorem on location of extrema, our strategy is to Find fxx,y and fyx,y, if the exist,…

Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Use derivative rules to compute f'(-1) given f (x) = -4x8-32x - 4.

A: f(x)=-4x8-32x-4Formula: xn'=n xn-1

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 − 3x2 −…

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Q: Explain how to find the critical numbers of a function.

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Q: Use the second derivative test todetermine whether f(x)=-2x³+6x2-3 has a localmaximum or…

A: Given,          fx=-2x3+6x2-3

Q: tion 1. Find the rule of the piecewise function

A: 1. From the graph given , the piecewise distribution of the function is as follows ,  fx=x+1 ,…

Q: use the first derivative test to characterize each critical value of f(x)=x3+6x2-18x+3 as a maximum,…

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Q: The function f(x) = 2a* - 39x2 + 240x + 10 has derivative f'(x) = 6x² – 78x + 240. f(x) has one…

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Q: 2. Let f(x) = Determine the exact location of any turning points. Use the second derivative to…

A: We can solve this as follows:

Q: Find the minimum of f(x) = 3 + 6*x + 5*x2 +3*x3 + 4*x4 in the range of [-2, 1]

A: the given function is f(x)=3+6x+5x2+3x3+4x4 find the derivative  f'(x)=6+10x+9x2+16x3 find the…

Q: Suppose that a function f(x, y) attains an absolute minimum at the point (2, -3), and an absolute…

A: Given that f(x,y)  attains absolute min at (2,-3) f(x,y)  attains absolute max at (-3,2) The new…

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is…

A: We find the critical points by solving f'(x)=0 Answer(a):  Critical numbers= -1.633 and 1.633

Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: Find the absolute maximum and absolute minimum of the function on the interval. f (x) = 5(x² -4)/z³,…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. = 9 + 81x – 3x³,…

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Q: Find the locations of local minimum and maximum of X⁹ x⁹-4x8 using the second derivative test. 32…

A: let f(x)=x9-4x8Differentiate with respect to x 9x8-32x7=0x7(9x-32)=0⇒x=0,x=329  are the critical…

Q: Consider the function f(x) = 2x° + 9x² – 108x +1 with - 6 <x < 4 | This function has an absolute…

A: Given, f(x) = 2x3 + 9x2 - 108x + 1  Plot the function on the interval -6&lt;= x &lt;= 4. For solving…

Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: Find the absolute maximum of x40-x20 on the interval [0,1].Find also its absulute maximum value

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Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: Determine all critical points for the function. 2) f(x) = 45x3 - 3x5 %3D

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the absolute minimum and absolute maximum values of f on the given Interval. f(x) = In(x2 + 3x…

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Q: At the point x 2, the function -8 2<x<* f(x) = |x-2 -< xs2 is (a) continuous and differentiable (b)…

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Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Find the absolute minimum and absolute maximum values of f on the given interval f(x) = x - In(2x),…

A: see next step

Q: Find the maximum and minimum values of the function y = V8 + x2 - 4x on the interval 3, 5|. (Use…

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Q: (3) Construct a function defined on the closed interval [0, 1] with no maximum and minimum. Justify…

A: The Extreme Value Theorem (EVT) says: If a function f is continuous on the closed interval a ≤ x ≤…

Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

Q: What is the maximum value of the function h(x) = 10x =—= 22² x² on the interval 0≤x≤ 40 and for what…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 17 + 4x -…

A: Given function f(x)=17+4x-x2   ; [0,5]

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 - 9x² –…

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Q: Find the relative extrema of the function and classify each as a maximum or minimum using the First…

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Q: The function f(x) = 2x³ − 33x² + 60x + 8 has derivative f'(x) = 6x² f(x) has one local minimum and…

A: Explanation of the answer is as follows

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 3x2 − 6x +…

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Q: the absolute minimum of f(x) = −x3 − 14x2 − 60x − 75 on interval [−7, −5]?

A: To find: The absolute minimum of fx=-x3-14x2-60x-75 in interval -7,-5. Calculation: The derivative…

Q: f = 2x – 3x²/3 on [-1,3].

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Q: Suppose you find the linear approximation to a differentiablefunction at a local maximum of that…

A: It is known that the linear approximation of a differentiablefunction at a local maximum of that…

Q: Find the critical points of the following function on the given interval. Identify the absolute…

A: Given: fx=2x3-3x2-36x+12 on -∞,∞ To evaluate the critical points find x where f'x=0.…

Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

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