Q72 / 150 · MHT CET 2011 · Mathematics

If $f(x)=e^{x} g(x), g(0)=2, g^{\prime}(0)=1$, then $f^{\prime}(0)$ is

  • A
    1
  • Correct answer
    B
    3
  • C
    2
  • D
    0

Solution

$f^{\prime}(x)=e^{x} g^{\prime}(x)+e^{x} g(x)$ $$ \begin{aligned} \Rightarrow \quad f^{\prime}(0)=e^{0} \cdot g^{\prime}(0)+e^{0} g(0) \\ =1 \cdot 1+1 \cdot 2 \\ \left[\because\left\{g^{\prime}(0)=1 \text { and } g(0)=2\right\}\right] \\ =1+2=3 \end{aligned} $$

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

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