JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)\) and \(f^{\prime \prime}(x)>0\) for all \(\mathrm{x} \in(0,3)\). If \(\mathrm{g}\) is decreasing in \((0, \alpha)\) and increasing in \((\alpha, 3)\), then \(8 \alpha\) is
- A \(24\)
- B \(0\)
- C \(18\)
- D \(20\)
Answer & Solution
Correct Answer
(C) \(18\)
Step-by-step Solution
Detailed explanation
\(g(x)=3 f\left(\frac{x}{3}\right)+f(3-x) \text { and } f^{\prime \prime}(x) > 0 \forall x \in(0,3)\) \(\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})\) is increasing function \( g^{\prime}(x)=3 \times \frac{1}{3} \cdot f^{\prime}\left(\frac{x}{3}\right)-f^{\prime}(3-x) \)…
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