Question

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

Answer 1

Answer

given,

$f(x) = 2 x^{1/5}$

interval = [-32, 32]        

differentiating the given equation

$f'(x) = \dfrac{d}{dx}(2 x^{1/5})$

$f'(x) = \dfrac{2}{5x^{4/5}}$

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.