Question

Determine whether the Mean Value Theorem applies to the function f(x)=3+x² on the interval [-2,1]. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.

Answer 1

Yes, the Mean Value Theorem applies.

f(x) = 3 + x²

f'(x) = 2x = (f(1) - f(-2))/(1 - (-2))

2x = (4 - 7)/3

6x = -3

x = -1/2