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

MCQ

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

A
No maxima and minima
✓
One maximum and one minimum
C
Two maxima
D
Two minima

✓

Answer

Correct option: B.

One maximum and one minimum

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

$f'(x) = 6{x^2} - 6x - 12$

Now $f'(x) = 0$ ==> ${x^2} - x - 2 = 0$ ==> $x = 2,\, - 1$

Now $f''(x) = 12x - 6$ ==> $f''(2) = + ve$, $f''( - 1) = - ve$

$\therefore$ Given function has one maximum and one minimum.

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