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

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

A

no maxima and minima

B

one maximum and one minimum

C

two maximum

D

two minima

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=2x^(3)-15x^(2)+36x+4impliesf^(`)(x)=6x^(2)-30x+36` …(i).
We know that for its maximum value
`f^(`)(x)=0.6x^(2)-30x+36=0implies(x-2)(x-3)=0impliesx=2,3`
Again differentiating equation (i), we get `f^(`)(x)=12x-30`
`impliesf^(``)(2)=24-30=-6lt0`.
Therefore `f(x)` is maximum at `x=2`.
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