Question

Can the mean value theorum be applied to the function f(x)=1/x^2 on the interval [-2, 1]? Explain.

Answer 1

No, it can not be applied.

Explanation:

f(x) = 1/x²

f(x) is a polynomial that is not continuous

As,

f(x) = 1/0 is undefines

Secondly, it is not differentiable (i.e. the derivative does not exists on the interval given)

Derivative of this function

f'(x) = (1)x^-2

= -2x^(-2-1)

= -2x^(-3)

= -2/x³

= -2/x³

f'(0) = -2/0 is undefined

Thus, mean value theorem can not be applied.