Q73 / 155 · WBJEE 2025 · Mathematics

The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has

A
two points of local maximum
B
two points of local minimum
Correct answer
C
one local maximum and one local minimum
D
neither maximum nor minimum

Solution

$\begin{aligned} & f^{\prime}(x)=0 \quad \Rightarrow x=-1,2 \\ & x=-1 \text { is local maxima } \\ & x=2 \text { is local minima }\end{aligned}$

Hence, the correct answer is option: 'C'.

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