The function f ( x ) = 2 x 3 - 3 x 2 - 12 x + 4 , has:

Question

The function $f (x) = 2 x^{3} - 3 x^{2} - 12 x + 4,$ has:

Smart Achievers · Accepted Answer

(3)

Ans. One maxima and one minima

Explanation:

We have, $f (x) = 2 x^{3} - 3 x^{2} - 12 x + 4$

$∴$ $f' (x) = 6 x^{2} - 6 x - 12$

Now, $f' (x) = 0$

$\Rightarrow$ $6 (x^{2} - x - 2) = 0$

$\Rightarrow$ $6 (x + 1) (x - 2) = 0$

$\Rightarrow$ $x = - 1$ and $x = 2$

On the number line for $f' (x)$ , we get

Hence, $x = - 1$ is the point of local maxima and $x = 2$ is the point of local minima.

So, $f (x)$ has one maxima and one minima.

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