CUET · MATHS · PYQ PAPER 2025
For the function \(f(x)=e^x+e^{-x}\)
(A) \(f^{\prime}(x)=e^x-e^{-x}\)
(B) The critical point is \(x=0\)
(C) The minimum value is 1
(D) \(x=0\) is the point of local minimum.
Choose the correct answer from the options given below:
- A (A), (B) and (D) only
- B (B), (C) and (D) only
- C (C) and (D) only
- D (A) and (D) only
Answer & Solution
Correct Answer
(A) (A), (B) and (D) only
Step-by-step Solution
Detailed explanation
\(f(x)=e^x+e^{-x}\) \(f^{\prime}(x)=e^x-e^{-x}\) Statement (A) is correct. \(f^{\prime}(x)=0 \implies e^x-e^{-x}=0\) \(e^{2x}=1 \implies x=0\) Statement (B) is correct. \(f(0)=e^0+e^{-0}=2\) Statement (C) is incorrect. \(f^{\prime\prime}(x)=e^x+e^{-x}\)…
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