CUET · MATHS · PYQ PAPER 2023
Which of the following functions satisfies Rolle's theorem?
- A \(f(x)=x, x \in[1,2]\)
- B \(f(x)=x^2, x \in[-1,1]\)
- C \(f(x)=x^3, x \in[-1,2]\)
- D \(f(x)=x^4, x \in[0,2]\)
Answer & Solution
Correct Answer
(B) \(f(x)=x^2, x \in[-1,1]\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^2\) Continuous on \([-1,1]\) Differentiable on \((-1,1]\) \(f(-1) = (-1)^2 = 1\) \(f(1) = (1)^2 = 1\) \(f(-1) = f(1)\)
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