Differentiation application

Question

find the value c guaranteEd by the mean value theorem for f (x) =x^2+x+3 on the interval [-1,2]

Answer 1

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

f' = 2x + 1

f(2) = f(b) = 9

f(-1) =f(a) = 3

 

2c + 1 = (9-3)/(3) = 2

2c = 2;  c = ½