An unknown constant Determine the value of the constant a for which the function x + 3x + 2 ifx + -1 f1x2 = c x + 1 a ifx = -1 is continuous at -1.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x3 − 6x2…

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Q: ind the intervals of increase, decrease, and concavity for the given function, as well as any local…

A: The given equation is  y=ln(x-x2) and we have to find the  intervals of increase, decrease, and…

Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2).  The graph of f is…

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Q: 7. Given the graph on the right (function is continuous on both ends). y a) Describe the end…

A: D) State the number of turning points. E) State an interval where the function is positive. F) State…

Q: True or false. if false, correct statement. if true, explain why.  a. if a function, f, is…

A: We consider the standard formulae and properties to answer the given true or false statements.

Q: Find all critical points where the second derivative equals zero or does not exist for the functions…

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Q: Find differentiable functions f and g that satisfy the specified condition such that xlim5 f(x) = 0…

A: Given: f(x) and g(x) which is differentiable and satisfy  limx→5 f(x)=0   and  limx→5 g(x)=0

Q: Show that the function g defined by yVF g(x, y) = y² + y² + √√x²¹ 2. is not continuous at (0, 0).…

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Q: Continuous Function Find a value for a so that the function - 1, x<3 [x² f(x) = \ 2ax,

A: fx=x2-1,     x&lt;32ax,        x≥3 Since the given function is a polynomial function for all x&lt;3…

Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2).The function f is…

A: We have to find the interval where it is increasing

Q: Function h is graphed. 4+ h 3- 1 -4 -3 -2 -1 1 2 3 4 -1- -2- -3 Find h(x) dx. h(x) dx = %3D నా ఈ 2)

A: Integration Question

Q: Find the absolute maximum and absolute minimum values of the function f(x) = 3x - 12 ln(2x) on the…

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Q: Identify the intervals where ƒ(x)=(1/4)​·x4+(1/3)​·x3−8·x2−16·x is increasing and where decreasing…

A: Given  The function is  f(x)=14x4+13x3-8x2-16x. function interval is [-4, 4] .

Q: A function F possesses three critical values, x=-3, 0 and x+3. The functions second derivative is…

A: You have the critical points with you along with the second derivative of the function. Put the…

Q: A function and its first and second derivatives are given. Use these to find each of the following.…

A: Given

Q: Consider the function on the interval (0, 2x). f(x) = sin(x) cos(x) + 7 (a) Find the open…

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Q: Question: Explain a method that could be used to find the absolute maximum and minimum values of a…

A: Derivative test   Determine the critical points (points where the derivative = 0 or the derivative…

Q: We know how to find the extreme values of a continuous function ƒ(x) by investigating its values at…

A: We have given continuous function fx.

Q: Consider the function on the interval (0, 2x). f(x) = * + cos x (a) Find the open intervals on which…

A: Given function is : fx=x2+cosx

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: Given, f(x) = x4 − 8x3 + 4 Differentiating f(x) with respect to x  f'(x) = 4x3- 24x2 + 0  (because…

Q: f (x) is a function with the domain (-00, -7) U (-7, 3) U (3, 0), and the graph of f "(x) given…

A: Given The domain of the function is (-∞, -7)U(-7,3)U(3,∞)  and graph of f''(x)

Q: 3. True or false? а. The values of a continuous variable are arrived at by counting. b. A continuous…

A: Discrete Discrete data set is the data in which value is countable and finite. Example {1,2,3,4,6}…

Q: First Derivative f(x,) – f(x,-1) 2h Error f'(x) = -f(x,) + 8ƒ(x,.) – 8ƒ(x}-1) + ƒ(x_-2) 12h f(x) =…

A: The required table is,

Q: Filling in a function value The domain of ƒ(x, y) = e-1/(x2 + y2) excludes (0, 0). How should ƒ be…

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Q: Mean Value Theorem. So I determined that this is continuous and differentiable at [1,7]. I just do…

A: Given function is  fx=1x

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Vhich function f(x) increases on the interval (-0, 0) but decreases on the interval (0, 0)? A. f (x)…

A: We can draw a graph of function by graph we can understand

Q: Electric Current. Suppose you have two electronic devices that have different currents when x = 2.…

A: The given function,   f(x)=a+3x+2x2if x&lt;24x2+6x+8if x≥2

Q: Find the absolute extrema of f on the given interval. (find the absolute maximum value and absolute…

A: Given, x2+ 4x+2, [-3,0]

Q: The continuous function has exactly one critical point. Find the x-values at which the global…

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Q: Graph of f(x) Graph of / A 1. In the interval 0<x< 1 of the first derivative test, f(x) is Ⓒa.…

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Q: Consider the function on the interval (0, 2«). (x) = sin x + cos x (a) Find the open intervals on…

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Q: A critical value such that f"(x)=0is called a stationary point. a) Show that both of the functions…

A: We have to find critical (stationary) points, maxima or minima and concavity.

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A: Suppose that x=c is a critical point of fx then, If f 'x&gt;0 to the left of x=c and f 'x&lt;0 to…

Q: An unknown constant Determine the value of the constant a forwhich the function

A: the given function is: fx=x2+3x+2x+1,    if   x≠-1a                       if  x=-1 we have to…

Q: X- a, =} 4, (bx +1, X -3

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Q: 5. The function f(x) has a derivative g(x), shown on the graph below. (2, 1) (0, 1) 1- 1 (4,-1)…

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Q: Question FHelp The stock price for a certain corporation can be approximated for the years 2010…

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Q: x² -4 %3D x2+1 Given the function: f(x) =

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Q: A function and its first and second derivatives are given. Use these to find each of the following.…

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Q: The participation rate is the number of people in the labor force divided by the civilian population…

A: Given that,  Let L(x) represent the size of the labor force in year x, and P(x) represent the…

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: Given : f(x)=x4+8x3-1 Take the first order derivative , we get : f'(x)=4x3+24x2. Therefore, we will…

Q: A function and its first and second derivatives are given. Use these to find each of the following.…

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Q: QI Find f'(x) for 1+ sec1(x) (x) = 1- csc-1(x) -csc (x) + sec (x) csc '(x) + sec '(x) V(x? - 1)(1-…

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Q: Determining unknown constants Let 5x - 2 ifx 6 1 glx2 = ca if x = 1 ax? + bx ifx 7 1. Determine…

A: Given that, gx=5x-2        if x&lt;1a                if x=1ax2+bx    if x&gt;1