Answer:
There is a value of in (-1, 1), .
Step-by-step explanation:
Let for , we need to prove that is continuous and differentiable to apply the Mean Value Theorem. Given that is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.
If is differentiable, then exists for all value of . By definition of derivative, we obtain the following expression:
(Eq. 2)
The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.
According to the Mean Value Theorem, the following relationship is fulfilled:
(Eq. 3)
If we know that , and , then we expand the definition as follows:
There is a value of in the interval (-1, 1), .