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Let h(x)=x^(m/n) for x in R , where m ...

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

A

no local extremums

B

one local maximum

C

one local minimum

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1
`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
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