Mathematics I (Calculus) - Old Questions

7. Verify Mean value theorem of f(x) = x³ − 3x + 3 for [−1,2].

Given,

f(x) = x³-3x+3 

Since, f(x) = x³-3x+3  is continuous on [-1, 2] and f’(x) = 3x²-3 so, differentiable on (-1, 2).

Thus f(x) = x³-3x+3 satisfy the both conditions for mean value theorem. So, there exist  such that

Clearly 

Hence, mean value theorem satisfied.