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

No, it can not be applied.

Step-by-step 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.