For the function f(x) = 6- 4x^2 on the interval [-1,8] the mean slope of this function is -252/9. By the mean value theorem, there exists a c in the open interval (-1,8) such that f '(c) is eqaul to the mean slope. What is the value of c and how do you find it?

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For the function f(x) = 6- 4x^2 on the interval [-1,8] the mean slope of this function is -252/9.

By the mean value theorem, there exists a c in the open interval (-1,8) such that f '(c) is eqaul to the mean slope. What is the value of c and how do you find it?

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Step 1

Calculation:

The given function is f(x) = 6 – 4x2 and the given interval is [– 1, 8].

It is given that the mean slope of the function on the interval is – 252/9.

Calculate the derivative of the function f(x) as follows.

Step 2

By mean value theorem the function f′(x) is equal to the mean slo...

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