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Consider the function f ( x ) = 3 − 5 x^2 on the interval [ − 2 , 8 ] . Find the average or mean slope of the function on this interval, i.e.

f(8)-f(-2)/8-(-2)=

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. For this problem, there is only one c that works. Find it.

Answer with explanation please and thanks!

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1 answer
  1. really? They gave you the actual formula.
    Just evaluate m = (f(8)-f(-2))/(8-(-2)) = ___
    now, since f'(x) = -10x, you want to find c such that
    -10c = m
    c = -m/10

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    oobleck

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