CUET · MATHS · PYQ PAPER 2025
For the function \(f(x)=2 x^3-3 x^2-12 x+5\), the difference of maximum and minimum value of \(f(x)\) is
- A 12
- B \(-15\)
- C 27
- D \(-3\)
Answer & Solution
Correct Answer
(C) 27
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2 - 6x - 12\) \(6x^2 - 6x - 12 = 0 \implies x^2 - x - 2 = 0\) \((x-2)(x+1) = 0 \implies x = 2, x = -1\) \(f(-1) = 2(-1)^3 - 3(-1)^2 - 12(-1) + 5 = -2 - 3 + 12 + 5 = 12\) \(f(2) = 2(2)^3 - 3(2)^2 - 12(2) + 5 = 16 - 12 - 24 + 5 = -15\) \(12 - (-15) = 27\)
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