Q134 / 225 · JEE Main 2002 · Mathematics

If $f(x+y)=f(x) \cdot f(y) \forall x \cdot y$ and $f(5)=2, f^{\prime}(0)=3$ then $f^{\prime}(5)$ is

  • A
    0
  • B
    1
  • Correct answer
    C
    6
  • D
    2

Solution

$$ f(x+y)=f(x) \times f(y) $$ Differentiate with respect to $x$, treating $y$ as constant $$ f^{\prime}(x+y)=f(x) f(y) $$ Putting $x=0$ and $y=x$, we get $f^{\prime}(x)=f^{\prime}(0) f(x) ; \Rightarrow f^{\prime}(5)=3 f(5)=3 \times 2=6$

Hence, the correct answer is option: 'C'.

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