CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=2 x^3-3 x^2-12 x+4\) has :
- A two points of local minimum
- B two points of local maximum
- C one maxima and one minima
- D no maxima or minima
Answer & Solution
Correct Answer
(C) one maxima and one minima
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2 - 6x - 12\) \(6x^2 - 6x - 12 = 0 \implies x^2 - x - 2 = 0 \implies (x-2)(x+1) = 0 \implies x = 2, x = -1\) \(f''(x) = 12x - 6\) \(f''(2) = 12(2) - 6 = 18 > 0\) (local minimum) \(f''(-1) = 12(-1) - 6 = -18 one maxima and one minima
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