If f(x)={(sin(x^(2)-3x),xle0 .^x+5x^(2...

If `f(x)={(sin(x^(2)-3x),xle0`
`.^x+5x^(2),xgt0`

A

f(x) has a local minima

B

f(x) has a local maxima

C

f(x) has point of inflection

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

1

f(x)=sin 0 =0
`f(x)^(+))rarr(0^(+))`
`f(0^(+))=underset(xrarr0)lim sin (x^(2)-3x)=underset(hrarr0)limsin (h^(2)+3h)rarr0^(+)`
Thus `f(x^(+)) and f(0^(-))gtf(x)`
Hence x =0 is point of manima

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