# Consider the function : f(x)=2x^2−2x^3+2⋅3xFind the average slope of this function on the interval (2,8)By the Mean Value Theorem, we know there exists a c in the open interval (2,8) such that f′(c) is equal to this mean slope. Find the value of c in the interval which works:

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Consider the function : f(x)=2x^2−2x^3+2⋅3x

Find the average slope of this function on the interval (2,8)

By the Mean Value Theorem, we know there exists a c in the open interval (2,8) such that f′(c) is equal to this mean slope. Find the value of c in the interval which works:

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Step 1

Calculation:

The given function is f(x) = 2x2 – 2x3 + 2·3x and the given interval is (2, 8).

Calculate the value of f (8) as follows.

Step 2

Calculate the value of f (2) as follows.

Step 3

The average slope of the function on the...

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