Let `h(x)=x^(m/n)` for `x in R ,` where +m and n are odd numbers and 0 less than m less than n Then `y=h(x)` has
a)no local extremums
b)one local maximum
c)one local minimum
d)none of these

Options

A. no local extremums
B. one local maximum
C. one local minimum
D. none of these

Answer

1

Explanation

`h(x) =(m)/(n)x^(m-n)/(n)=(m)/(n)x^(even)/(odd)`
As h'(x) is undefined at x=0 and h(x) does not change its sign in the neightborhood there are no extremums