CUET · MATHS · PYQ PAPER 2023
For \(x \in[-2,2]\), let \(f(x)=x^2+2\).
A. \(f(x)\) is continuous in \([-2,2]\)
B. \(f(x)\) is differentiable in \((-2,2)\)
C. \(f(-2)=f(2)=6\)
D. \(f^{\prime}(1)=0\)
Choose the correct answer from the options given below:
- A A, D only
- B B, C, D only
- C A, B, C, D only
- D A, B and C only
Answer & Solution
Correct Answer
(D) A, B and C only
Step-by-step Solution
Detailed explanation
A. \(f(x)\) is a polynomial, thus continuous on \([-2,2]\). B. \(f'(x) = 2x\), thus differentiable on \((-2,2)\). C. \(f(-2) = (-2)^2+2 = 6\). \(f(2) = (2)^2+2 = 6\). D. \(f'(1) = 2(1) = 2\). A, B, C are true; D is false. A, B and C only
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