CUET · MATHS · PYQ PAPER 2025
Which of the following functions has a local minima at \(x=0\) ?
(A) \(f(x)=x^3\)
(B) \(f(x)=|x|\)
(C) \(f(x)=x^2\)
(D) \(f(x)=x^{-2}\)
Choose the correct answer from the options given below :
- A (A), (B) and (C) only
- B (D) only
- C (B), (C) and (D) only
- D (B) and (C) only
Answer & Solution
Correct Answer
(D) (B) and (C) only
Step-by-step Solution
Detailed explanation
For \(f(x)=|x|\): \(f(0)=0\). For \(x \neq 0\), \(|x|>0\), thus \(f(x) \ge f(0)\). Local minima at \(x=0\). For \(f(x)=x^2\): \(f'(x)=2x\), \(f'(0)=0\). \(f''(x)=2\), \(f''(0)=2>0\). Local minima at \(x=0\). The correct option is (B) and (C) only.
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