CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=4 x^3-7 x^2\) has point(s) of local minima at :
- A \(x = 0\)
- B \(x=0,-\frac{7}{6}\)
- C \(x=\frac{7}{6}\)
- D \(x=-\frac{7}{6}\)
Answer & Solution
Correct Answer
(C) \(x=\frac{7}{6}\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 12x^2 - 14x\) \(f'(x) = 0 \Rightarrow 2x(6x-7)=0 \Rightarrow x=0, x=\frac{7}{6}\) \(f''(x) = 24x - 14\) \(f''(0) = 24(0) - 14 = -14 \(f''(\frac{7}{6}) = 24(\frac{7}{6}) - 14 = 28 - 14 = 14 > 0 \Rightarrow\) Local minimum at…
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