MCQ
The function $f(x) = 2{x^3} - 3{x^2} - 12x + 4$ has
- ANo maxima and minima
- ✓One maximum and one minimum
- CTwo maxima
- DTwo minima
✓
Answer
Correct option: B.
One maximum and one minimum
b
(b)$f(x) = 2{x^3} - 3{x^2} - 12x + 4 ,$
(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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