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If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then...

If `f(x)=x^3+bx^2+cx+d` and 0<`b^2`<`c`, then

A

f(x) is strictly increasing function

B

f(x) has a local maxima

C

f(x) is a strcrly decreasing function

D

f(x) is unbounded

Text Solution

Verified by Experts

The correct Answer is:
A
If `f(x)=x^3+bx^2+cx+d rArr f'(x)=3x^2 + 2bx + c `
Let `D_1` be the discriminant of f'(x)`=3x^2+2bx+c.` Then
`D_1=4b^2=12c=4(b^2-c)-8c lt 0 " "[therefore b^2 lt c and c gt 0 ]`
`f'(x) gt 0 for all x in (-oo,oo)`
`rArr` f(x) is strictly increasing function on`(-oo,oo)`
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