JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a thrice differentiable odd function satisfying \(f^{\prime}(\mathrm{x}) \geq 0, f^{\prime}(\mathrm{x})=f(\mathrm{x}), f(0)=0, f^{\prime}(0)=3\). Then \(9 f\left(\log _{\mathrm{c}} 3\right)\) is equal to _______.
- A 32
- B 34
- C 36
- D 38
Answer & Solution
Correct Answer
(C) 36
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{f}(\mathrm{x}) \\ & \Rightarrow \mathrm{f}^{\prime}(\mathrm{x}) \cdot \mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{f}^{\prime}(\mathrm{x}) \cdot \mathrm{f}(\mathrm{x}) \\ & \Rightarrow…
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