How do you determine all values of c that satisfy the mean value theorem on the interval [-3,-2] for #f(x) = x^2 + 4x + 2#?

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Answer 1 · 2017-12-19T17:52:59

Solve #f'(x)=(f(-2)-f(-3))/((-2)-(-3))# on the interval #(-3,-2)#

The conclusion of the mean value theorem says:

there is a #c# in #(a,b)# with #f'(c) = (f(b)-f(a))/(b-a)#.

To find that #c# (or those #c#'s, find the equation and solve it.

In this case, you should get #c=-5/2#