AP EAMCET · Maths · Continuity and Differentiability
If \(f: R \rightarrow R\) is a differentiable function such that \(f(x+y)=f(x) . f(y)\) for all \(x, y \in R\) and if \(f^{\prime}(4)=24\) and \(f^{\prime}(0)=3\), then \(f(4)=\)
- A 72
- B 5
- C 11
- D 8
Answer & Solution
Correct Answer
(D) 8
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } x=4, y=0 \Rightarrow f(4+0)=f(4) \cdot f(0) \\ & \Rightarrow \quad \begin{aligned} f(4) & =f(4) f(0) \Rightarrow f(0)=1 \\ f^{\prime}(4) & =\lim _{h \rightarrow 0} \frac{f(4+h)-f(4)}{h} \\ & =\lim _{h \rightarrow 0} \frac{f(4) f(h)-f(4)}{h}=\lim…
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