Classwork Session 4 Practice Problems: (1) The graph below shows the graph y = f(x) of a function f(x). Sketch the graph y =f 0 (x) of the derivative. (Hint: think about where f 0 (x) is positive, negative, or zero; and think about where it is large in magnitude or small in magnitude. Do not try to do it algebraically, by guessing a formula for the function being graphed here.) %3D

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A: We are answering only the first three subparts as per our honor code. The graph of the derivative of…

Q: Free Response- Suppose that the derivative of a function, f(x), is given by the equation f'(x) =…

A: Given derivative of function f(x) is f'(x)=-2x(x+2)2(x-3)⇒f'(x)=-2(x4+x3-8x2-12x)              (1)…

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Q: The graphs below show the first and second derivatives of a function y = f(x). Draw a possible graph…

A: The slope of y=f(x) is as shown in figure (1). From the figure (1) The graph of f'(x) is decreasing…

Q: ind the derivative of the function. HINT [See Examples 1 and 2.] g(x) =  1/ x4 +  1/ x8   g'(x) =

A: Consider the given function as gx=1x4+1x8. We have to find the derivative g'x of the above function.…

Q: Find the derivative of the function. HINT [See Examples 1 and 2.] g(x) = x−2 − 5x−1 − 6

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Q: %3D Find an equation of the tangent line to the graph of the function f(x) = 12 - 5e* at the point…

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Q: The graphs below show the first and second derivatives of a function y = f(x). Find a possible graph…

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Q: Find the derivative of the function. HINT [See Examples 1 and 2.] g(x)=1/x - 1/x7

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Q: Can i get help step by step please

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Q: The graph of gʻ(x), the derivative of a function g(x) is pictured below on the closed interval…

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Q: The graph of a function f(x) is shown below. Sketch the graph of its derivative f’(x).

A: Definition: Let f(x) be a function. f(x) is said to be increasing over some interval if f'(x)>0…

Q: The graphs below show the first and second derivatives of a function y = f(x). Select a possible…

A: To determine the graph of the function.

Q: HIYON IV. CALABARZO Learning Task 5: Find the derivative of the following function using the formu-…

A: Given: f(x)= 3x2-10x+6

Q: 1 y = In _3 x + 1

A: Given:

Q: Find the derivative of the function. HINT [See Examples 1 and 2.] h(x) = 6/x - 2/x3 +1/x4

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Q: Find the derivative of the function. HINT [See Examples 1 and 2.] g(x) =  1/x  - 1/x^2    g'(x) =

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Q: Compute the derivative function f'(x) algebraically. HINT [See Examples 2 and 3.] f(x) = 6x2 + x…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: The graph of function f(x) is shown below. At which value of z is the derivative of the function…

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Q: The graphs below show the first and second derivatives of a function y = f(x). Select a possible…

A: The f' function has to be the curve shown below: Let us say f' = sin x

Q: Please provide me with the solution and work to the question. Please try to dumb it down so I can…

A: (a) The f(x) is maximum at x = -4 and minimum at x = 2.So x = -4 and 2 are the critical…

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: Free Response- Suppose that the derivative of a function, f(x), is given by the equation f"(x) =…

A: Given: f'(x)=-2x(x+2)2(x-3) f(-1)=-2 f"(-1)>0

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Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = (5x - 1)-2 f'(x) =

A: f(x) = (5x-1)^-2 f'(x) = -2(5x-1)^-3 * d/dx (5x-1) f'(x) = -10(5x-1)^-3

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Q: Calculate the derivative of the function. HINT [See Example 1.] 1 f(x) 5x - 3 f'(x) =

A: Answer: f'(x)=-55x-12

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A: Given

Q: Consider the function, whose graph y = f(x) is shown below. -3 -2 What is the set of values of x E…

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Q: Calculate the derivative of the function. HINT [See Example 1.] g(x) = (2x2 + x + 4)−3 g'(x) =

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Q: 2) Consider the function defined by g(x) = 5x - 4. You may use the graph of this function to…

A: Recall: Derivative(|x|)=xx

Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = (x – 4)-1 f'(x) =

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Q: The graph of the derivative of a function is given. Sketch the graphs of two functions that have the…

A: From the given graph, it is observed that the derivative of the function constant and its constant…

Q: Find the derivative of the function. HINT [See Examples 1 and 2.] g(x) = x-2 - 3x-1- 2

A: Given function is

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A: 1. fx=3x2-5x   fx0=3x02-5x0…

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A: Given,          fx=x2-6x-6;  1,6         The first derivative of f is f'x=2x-6

Q: Compute the derivative function f'(x) algebraically. HINT [See Examples 2 and 3.] 9x f(x) b (k # 0)…

A: Given:- The function is, f(x)=9xk-b (k≠0) To compute: - Ther derivative of the given function f'(x)…

Q: 1le Identify the graphs A (blue), B(red) and C (green) as the graphs of a function f(x) and its…

A: When f'>0 then function increasing  then graph of f' lies above x axis  when f'<0 then…

Q: (9 points) For the function whose graph is shown below, find the value(s) of x at which t derivative…

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Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: The graph shown is the 1st derivative of function where its domain is R 2 -10 -8 -6 पि A value where…

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Q: Inclass (Example 3: Find the equation of the tangent line to the graph of f(x) = r³ +4 at r =-1.

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Q: Graph O in the red box below depicts the graph of a function f. Which of the other graphs A, B, C,…

A: An even function is symmetric to y - axis  An odd function is symmetric to origin

Q: Find the derivative of the function. HINT [See Examples 1 and 2.]   h(x) =  7/ x −  2/ x3 +  1/ x4…

A: The given function hx=7x-2x3+1x4      =7x-1-2x-3+x-4 Differentiate with respect to x using the…

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A: Given a graph of function f(x) , need to solve the questions based on the graph

Q: -54 -3 -2 -2 This is the graph of the derivative f '(x). The function f(x) (whose graph you do not…

A: Graph is                                             From the given graph of derivative f'(x) we…

Q: The graphs of four derivatives are given below. Match the graph of each function in (a)-(d) with the…

A: shows f'(x)>0 at first , then f'(x)<0, then again f'(x)>0, then f'(x)<0 So f(x) is…

Q: Find the function with the given derivative whose graph passes through the point P. 4 + 5 - 12x?,…

A: Given that, g'x=4x5+12x2,  P1, 7

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.