1. The graph shows the derivative of f, f'. Identify the intervals when f is increasing and decreasing. Include a justification statement. f'(x) Increasing: Decreasing:

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: . Find the  n th derivative of each function by calculating thefirst few derivatives and observing…

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Q: a. Find the derivative of f at x. That is, find f'(x). b. Find the slope of the tangent line to the…

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Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Let f(x) = ? The slope of the tangent line to the graph of f(x) at the point (-2, -) is The equation…

A: Solution:Givenf(x)=9xTo find the slope of the tangent line to the graph of…

Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

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Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A: We will do all three parts.

Q: Use the graph of the first derivative function  f'(x) to find the interval  on which function is…

A: Given: the graph of the first derivative function  f'(x).

Q: Determine the derivative of the following function by applying the quotient rule.…

A: The given function is: h(x)=ln (x2+x)x2+1 The quotient rule for the derivative is given by:…

Q: All boxes with a square base, an open'top, and a volume of 160 ft have a surfac the surface area…

A: The surface area of the box S(x)=x2+640x ...............(1) differentiate with respect to x,…

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: 3. Below is the graph of y = f'(x), which is the derivative for some function f. Using the graph of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: The function f whose derivative is f'x) = (x – 1)e"* is decreasing on (-00, 1). Select one: O True O…

A: We Know that the derivative of a function may be used to determine whether the function is…

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: 5. Use the definition of the derivative to find f'(x) if f(x)== x-÷ (i.e. ƒ(x)= . (i.e. f(x +h)-…

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Q: Use the Quotient Rule to show that the Powers of x Rule applies to negative integer powers. That is,…

A:

Q: Find the derivative of f(x) with respect to x ( f(x) = cos(x), find the f(x) by using the…

A: Given;  f(x)=cosx.

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: Find all possible functions f with the given derivative.  f'(x)= ex

A: The given derivative function is,

Q: 2) Suppose the graph of f (x) and the graph of its derivative f '(x) are shown below. Find an…

A: From the graph of f(x) , at x=1, f(x)=1 From the graph of f'(x), at x=1, f'(x)=-2

Q: p(x) = In(x)^/x

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: f(x) = x In x

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Q: g(u) u +1

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Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

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Q: The définition of the first derivative of a function f(x) is:

A: Explanation of the answer is as follows

Q: 2) Suppose the graph of f (x) and the graph of its derivative f'(x) are shown below. Find an…

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Q: Suppose the only information we have about a function fis that f(1)=2 and the graph of its…

A: Ti find the linear approximation.

Q: Suppose the derivative of f is f '(x)=- At what values of x does the f does have a x slope of -4.

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Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

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Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: 7. Determine the derivative of the function with respect to x. ソミx

A:

Q: Find a formula for (f-l)(x) given that f is one-to-one and its derivative satisfies the equation…

A: We can solve this using idea of function and definition of inverse of function

Q: 2. Use the second derivative to find the inflection points and the intervals on which f(x) is…

A: For inflection point, Put f"(x)=0. For concave upward, f"(x) &gt; 0. For concave downward, f"(x)…

Q: Let f(x) : 3x Using the limit definition of the derivative, find the equation x +1 of the line…

A: Given data: The given function is f(x)=3x/(x+1). The given point is (a, b)=(2, 2). The expression…

Q: When given a function f(x), describe (in common language) what the derivative function f'(x) is and…

A: Solution 1:   The derivative of a function f(x) of a variable x is a measure of the rate at which…

Q: What is the derivative of the exponential function a x, a &gt;0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative of f with respect to x of f(x) = In x'

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Q: Below is the graph of y=f'(x), for some function f. Using the graph of the derivative of f,…

A: We will find out the required critical points.

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…