CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=x e^x\) increases only for:
- A \(x \leq 1\)
- B \(x \geq 1\)
- C \(x \leq-1\)
- D \(x \geq-1\)
Answer & Solution
Correct Answer
(D) \(x \geq-1\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 1 \cdot e^x + x \cdot e^x = e^x(1+x)\) \(e^x(1+x) \ge 0\) \(1+x \ge 0\) \(x \ge -1\)
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