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Which one the following statements is co...

Which one the following statements is correct?

A

f(x) has local minima at more than one point in `(-oo,oo)`

B

f(x) has local maxima at moer than one point in `(-oo,oo)`

C

f(x) has local minimum at one point only in `(-oo,oo)`

D

f(x) has neither maxima nor minima in `(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
f(x) has local minimum at one point only in `(-oo,oo)`.
`f(x)={{:(2x-1",",xlt1),(2x+1",",xge1):}`
Clearly, for `(xgt1),f'(x)gt&" for "(xlt1)`
`(x=(1)/(2))` is the point of local minima
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