The graph of a linear function f is given. y X 1 (a) Find the rate of change of f. (b) Express f in the form f(x) = ax + b. f(x) = 21

Q: The average rate of change of a function f(x) = x² between x = 2 and x = 4 is %3D average rate of…

A: The given function  f(x) = x2 The average rate of change of function over interval [a, b] is given…

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given function is fx=x3

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

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Q: Sketch the graph of a function f such that f′ > 0 for all x and the rate of change of the…

A: Given A function f with f’>0 and rate of change is decreasing.

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: We have, f is the focal length (constant) of a convex lens and an object is placed at a distance p…

Q: Let f be the linear function f(x) = -2x + 5. (a) The rate of change of f is (b) The graph of f is a…

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Q: 12. f(x)=5-2/5x  express it in the form f(x) =ax+b and state the rate of change of the function.

A: Given:  fx=5-25x To Find:  To express the given function into the form, fx=ax+b, and to state the…

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: Given the function g(x) = -x² – 5x + 8, determine the average rate of change of the function over…

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Q: 2х + 1 f(x) : х+ 2

A: Given:…

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: The graph of a linear function is shown. Find the rate of change of y with respect to x.

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Q: Find the instantaneous rate of change of the function at the specified value of x. f(x)=(x−3)/(x+5)…

A: Given data:     The given function is: f(x)=(x-3)/(x-5).   The expression for the rate change of the…

Q: Consider the function f(x) = x2 − 3x + 3. (a) Find f' (x) from first principles. (b) Find the rate…

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Q: Find the average rate of change of g(x) = - 5x – 1 between the points (-4,19) and (3,-16)

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Q: Given F(x)=1/X+2,  find the average rate of change of  f(x) on the interval [2,2+h

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Q: find the average rate of change of the function from x=1 to x=2  f(x) = -(2/x^2)   average rate…

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Q: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

A: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

Q: Solve the problem. Compute the instantaneous rate of change of the function at at x = a. f(x) = -8x2…

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Q: f (x) = 2x² – 3x + 2 Find the instantaneous rate of change at x = 2

A: The instantaneous rate of change of a function is given by the first derivative of the function. The…

Q: Use Definition 1 or 2 to find the instantaneous rate of change of the function at the given value…

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Q: Find the average rate of change of the function from x=1 to x=2.   f(x)= -6/x^2

A: As we know that the expression for the average rate of change of the function: Average rate of…

Q: The table shows a linear relationship between x and y. What is the rate of change of y with respect…

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Q: Let ​g(x)=3x2−2. Find the average rate of change of the function as x changes from −1 to 7. the…

A: SOLUTION-

Q: Consider the function f (x) = -x² + 10. Find the average rate of change in the interval -5 <x < -1.

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Q: Given a function f(x)=e^2x−e^x+1, what value of x makes the relative rate of change equal to one?

A: We first find f'(x) using chain rule f(x)=e2x−ex+1f'(x)=2e2x-ex

Q: The function y = f(x) is graphed below. What is the average rate of change of the function f (x) on…

A: Average rate of change of function f(x) in the interval [a, b] is as follows. Ax=fb-fab-a

Q: 3. Determine the x-value(s) for which the function g(x) = In|x² +3x| has an instantaneous rate of…

A: Given function is Differentiating both sides with respect to x, we get

Q: a. What is the slope of the constant function y = k?b. What is the rate of change of a constant…

A: If function is given as y=fx Then the slope of the function is given as the first derivative of the…

Q: f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 6 units per…

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Q: Let f be the linear function f(x) = -3x + 7. (a) The rate of change of f is (b) The graph of f is a…

A: Objective is to fine the rate of change , slope and y-intercept Intercept.

Q: For which value of x is the instantaneous rate of change in the function graphed below negative? 2 1…

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Q: The graph of a linear function is shown. Find the rate of change of y with respect to x

A: We can find the rate of change as below.

Q: The volume of a container is given by V = ar² ( h + 1) cm³ , where r(radius), h(height) are…

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Q: Determine the value of k so that the rate of change of the function f (x) = 4x² + kx – 7 is 7 when…

A: Answer

Q: how do you find the average rate of change of the function over the given interval? y = -3x3 + 2x2…

A: Calculation:The given function is y =  – 3x3 + 2x2 – 4x + 1. Let y = f(x).Substitute x = – 2 in the…

Q: Given a function f(x) = e2 - e +1, 2.0 calculate the relative rate of change when x = 3. Give your…

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Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = x² –…

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

Q: -2x2 1. Find the average rate of change of f (x): on the interval [-2,2]. %3D (x-3)(2x+1)

A: topic - average rate of change of function over the interval

Q: Consider the function: g(x) = 2x + 6x 2 Find the average rate of change of g(x) between the points =…

A: We will Use the average rate of change formula to solve our given problem.

Q: Suppose that f(x)=-7x2 + 8 (A) Find the slope of the line tangent to f(x) at x=2 (B) Find the…

A: To determine the following for the function f(x) = -7x2 + 8:Part a) Slope of tangent at x = 2.Part…

Q: The table gives the profit, P of a fast food chain, where P is in millions of dollars and t is in…

A: Given,

Q: g(x)=-5x+2 find average rate of change of the function between x=a and x=a+h

A: Average rate of change of a function x=m to x=n is given as:

Q: (x) What is the average rate of change of the function f(x) = 2° – 4 from x = 0 to x = 3? %3D - 3 2…

A: Given : f(x) = 2x - 4 From x = 0 to x = 3.   To find the average rate of change of the function.

Q: y is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do…

A: Linear Function  Y= mX+c  m= slope of function  c = Y intercept

Q: The instantaneous rate of change for the function Y=x^2+2x,  at x= 3

A: The rate of change of any function is given by dydx  at any point x=x0 ,that is derivative of 'y'…

Q: Given the function g(x) = -x2 – 3x +5, determine the average rate of change of the function over the…

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Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: In the question, we were given the formula related to the length of the convex lens. Its equation is…

Q: f(x)= 12x^3 -20x^4 Find the rate of change with respect to x

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Q: – 3x Find the relative rate of change of f(x) = 6+ 3 e -

A: