CUET · MATHS · PYQ PAPER 2025
If the function \(f(x)=2 x^3+9 x^2+12 x-1\) is given, then \(f(x)\) has
- A Local minima at \(x=-1\)
- B Local maxima at \(x=\frac{3}{2}\)
- C Neither maxima nor minima at \(x=-2\)
- D Minimum value of \(f(x)\) is \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(A) Local minima at \(x=-1\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2 + 18x + 12\) \(6x^2 + 18x + 12 = 0 \Rightarrow x^2 + 3x + 2 = 0 \Rightarrow (x+1)(x+2) = 0\) \(x = -1, x = -2\) \(f''(x) = 12x + 18\) \(f''(-1) = 12(-1) + 18 = 6\) \(f''(-1) > 0\), so \(f(x)\) has a local minimum at \(x = -1\).
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