8. Given the graph of f(x), sketch a plausible graph of f'(x). Provide an explanation for the graph that you constructed.

Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

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Q: Find the equation of the function f whose graph passes through the point (0, 8/3) am whose…

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Q: f (x) = 2л2 + 5

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Q: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

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Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: ) Find an CIuation of the line tangent to the graph of Gec)=6e3X x tal dou2 o the Point (0,6). at

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Q: An equation of the line tangent to the graph of f(x)= x(1-2x) at the point (1,-1) is

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Q: If the slope of the tangent at any point of a function f passing through the point (2,-2) Is e^(-…

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Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

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Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Given: The  slope of  a curve:   To determine: The equation of the curve f(x)

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= x² + √x at x=1?

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Q: Find an equation of the tangent line to the graph of f(x) = 4 - x2 at the point (-1,3).

A: Solve for the equation

Q: Here is the graph of the second derivative of a function g(x). g"(x) Where does g(x) have a point of…

A: Inflection point is at that x value where the double derivative of the function is 0.

Q: 1 ソ= 1- x

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: The tangent lines to the graph of f(x) =x² grow steeper as x in- creases. At what rate do the slopes…

A: Given function is, f(x)=x2

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Sketch the graph of the derivative for function shown.

A: Graph has a horizontal tangent between x=-2 and x=-1, at x=0 and at x=2.9, Therefore graph of f'…

Q: Find the equation of the tangent to the graph of f(x) = x-3 at the point (5, 4). Start by evaluating…

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Q: he figure shows the graph of the derivative f' of a function f. yA y= f'(x) -2/

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

Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Sketch the graph of the derivative for function shown.

A: Plot the derivative for -∞<x<0. The function f(x) is constant in the interval -∞<x<0 so…

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

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Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Suppose the derivative of the function y​f(x) is (x-1)^2(x-5)(x-2). At what​ points, if​ any, does…

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Q: Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use…

A:

Q: 3. Use the second derivative to find the location of all local maxima for the following function and…

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Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

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Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: f'(x) at x if f(x) = csc³(x).

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: Find the equation of the line tangent to the graph of f(x) = ₂ at x = 3.

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Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: Find an equation of the tangent line to the graph of y = f(x) when x = 2 if f(2) = -6 and f'(2)= 5.…

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Q: f(x)

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Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Using integration.

Q: 5. Sketch the graph of y = x3 + 5x2 + 3x - 4 by using the properties of the derivative.

A: Find f' (x) then we check f(x) increasing Or decreasing.

Q: 13. Sketch the derivative f'(x) for this graph of f (x):

A: Graph drawing of f'(x) problem...

Q: Find the function with the given derivative whose graph passes through point P. F'(x)=2x-3, P(5,5)

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

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

Q: The slope of the line tangent to the graph of position as a function of time at t = to

A: The slope of the line tangent is in the form of a difference quotient approach t=t0 is, m=ft-ft0t-t0

Q: Sketch the graph of the function f whose derivative has the given graph

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 4 +9 In…

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Q: 3. If the graph of y=fcx) has a horizontal tangent at x=a, what is happening at this point ? I…

A: For a function ; a point is considered. A horizontal tangent exists at this point which means that…

Q: Find all the points on the graph of y=f(x) at which the tangent line has the given slope.…

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