Given the function f(x)=(x-4)^2-1, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,0] and find the c?

1 Answer
Aug 14, 2016

c=3/2

Explanation:

Mean value theorem states that for a function defined and continuous on [a,b] and continuously differentiable on (a,b) then there exists some a < c < b such that

f'(c) = (f(b)-f(a))/(b-a)

With a = 0 and b = 3 we have

(((3-4)^2-1) - ((0-4)^2-1))/3 = -5

f'(x) = 2(x-4)

implies f'(c) = 2(c-4)

2c - 8 = -5

2c = 3 implies c = 3/2