CUET · MATHS · PYQ PAPER 2025
Let \(f(x)=x^3-6 x^2+9 x-8\) be a function, then which of the following statements are TRUE?
(A) \(f^{\prime}(x)=3(x-1)(x-3)\)
(B) The critical points of the function are \(x=1\) and \(x=3\)
(C) \(x=1\) is the point of local minimum
(D) The local maximum value is -4
Choose the correct answer from the options below :
- A (A), (B) and (C) only
- B (A), (B) and (D) only
- C (B), (C) and (D) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(B) (A), (B) and (D) only
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{d}{dx}(x^3-6 x^2+9 x-8) = 3x^2-12x+9\) \(f'(x) = 3(x^2-4x+3) = 3(x-1)(x-3)\) (Statement (A) is TRUE) Set \(f'(x)=0 \Rightarrow 3(x-1)(x-3)=0 \Rightarrow x=1, x=3\) (Statement (B) is TRUE) \(f''(x) = \frac{d}{dx}(3x^2-12x+9) = 6x-12\) \(f''(1) = 6(1)-12 = -6\)…
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