f(x) is differentiable on the interval. So, you know there is a c such that
f'(c) = (f(2)-f(0)/(2-0) = (-1-2)/2 = -3/2
So, just solve for c in
4c-5 = -3/2
c = 7/8
as a check, view
http://www.wolframalpha.com/input/?i=plot+y+%3D+2x^2-5x%2B1+and+y+%3D+%28-3%2F2%29%28x-7%2F8%29+-+59%2F32
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = 2x^2 − 5x + 1, [0, 2]
If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
1 answer
1 answer