CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=\frac{x^4}{4}-\frac{x^2}{2}\) has
- A 2 points of local maxima
- B 2 points of local minima and one point of local maxima
- C 1 point of local minima and 2 points of local maxima
- D 1 point of local maxima and 1 point of local minima
Answer & Solution
Correct Answer
(B) 2 points of local minima and one point of local maxima
Step-by-step Solution
Detailed explanation
\(f'(x) = x^3 - x\) \(x^3 - x = 0 \implies x(x^2 - 1) = 0 \implies x = -1, 0, 1\) \(f''(x) = 3x^2 - 1\) \(f''(0) = 3(0)^2 - 1 = -1 \(f''(1) = 3(1)^2 - 1 = 2 > 0\) (Local minimum)…
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