Question

Determine whether the Mean Value Theorem applies to the function f(x)=2x^1/5 on the interval [-32, 32]

Answer 1

given,

`f(x) = 2 x^(1/5)`

interval = [-32, 32]

differentiating the given equation

`f'(x) = (d)/(dx)(2 x^(1/5))`

`f'(x) = (2)/(5x^(4/5))`

hence, the above solution is not defined at x = 0

and x = 0 lie in the given interval i.e. [-32, 32]

so, at x = 0 the function is not differentiable.

Hence, mean value theorem does not apply to the given function.