1.

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

Answer»

f(x) has a LOCAL minima
f(x) has a local maxima
f(x) has POINT of inflection
NONE of these

Solution :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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