JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f: R \rightarrow R\) satisfy \(f(x+y)=2^{x} f(y)+4^{y} f(x), \forall x\), \(y \in R\). If \(f(2)=3\), then \(14 \cdot \frac{f^{\prime}(4)}{f^{\prime}(2)}\) is equal to
- A \(246\)
- B \(250\)
- C \(248\)
- D \(251\)
Answer & Solution
Correct Answer
(C) \(248\)
Step-by-step Solution
Detailed explanation
Put \(y=2\) \(f(x+y)=2^{x} \cdot f(y)+4^{y} \cdot f(x)\) \(f(x+2)=2^{x} \cdot 3+16 f(x)\) \(f^{\prime}(x+2)=16 f^{\prime}(x)+3 \cdot 2^{x} \ln 2\) \(f^{\prime}(4)=16 f^{\prime}(2)+12 \ln 2\) ...\((i)\) \(f(y+2)=4 f(y)+3 \cdot 4^{y}\)…
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