y = - x ^2/ 2 + x - 1/ 2 ; [-2, 1] , find the value of c that satisfies the mean value theorem

Question

I am trying to understand this calculus problem but I am stuck. Please help me.

Answer 1

f(x) = -x²/2 + x - 1/2 is continuous on [-2,1] and is differentiable on        (-2, 1).

 

Therefore, the Mean Value Theorem applies.

 

By the Mean Value Theorem, there is at least one number, c, in the interval (-2,1) such that f'(c) = (f(1) - f(-2))/(1-(-2))

 

-c+1 = (0 - (-4.5))/3

 

-c+1 = 1.5

 

     c = -1/2