Mathematics I (Calculus) - Old Questions

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

Given,

f(x) = x³-3x+2 

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

Thus f(x) = x³-3x+2 satisfy the both conditions for mean value theorem. So, there exist  such that

Clearly, 

Hence, mean value theorem satisfied.