MCQ
The function f(x) = 2x3 - 3x2 - 12x + 4, has:
- ATwo points of local maximum.
- BTwo points of local minimum.
- COne maxima and one minima.
- DNo maxima or minima.
✓
Answer
- One maxima and one minima.
Solution:
We have, f(x) = 2x3 - 3x2 - 12x + 4
⇒ f'(x) = 6x2 - 6x - 12
⇒ f'(x) = 6(x2 - x - 2)
⇒ f'(x) = 6(x + 1)(x - 2)
Find the critical points by equating f'(x) to 0.
$\therefore$ f'(x) = 0
⇒ 6(x + 1)(x - 2) = 0
⇒ x = -1 and x = +2
From the above number line, we can conclude that, x = -1 is point of local maxima and x = 2 is point of local minima.
Thus, f(x) has one maxima and one minima.
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