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The function f(x)=2x^(3)-3x^(2)-12x-4 ha...

The function `f(x)=2x^(3)-3x^(2)-12x-4` has

A

no maxima and minima

B

one maximum and one minimum

C

two maxima

D

two minima

Text Solution

Verified by Experts

The correct Answer is:
B
The given function is
`f(x)=2x^(3)-3x^(2)-12x+4`
On differentiating w.r.t `x` we get
`f'(x)=6x^(2)-5x-12`
Either maxima or minima `f'(x)=0`
`impliesx^(2)-x-2=0impliesx=2-1`
Again differentiating `f"(x)=12x-6`
`impliesf"(2)=+ve,f"(-1)=-ve`
`:.` Given function has one maximum and one minimum.
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