MHT CET · Maths · Functions
If \(f(x)=e^{x} g(x), g(0)=2, g^{\prime}(0)=1\), then \(f^{\prime}(0)\)
is
- A 1
- B 3
- C 2
- D 0
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=e^{x} g^{\prime}(x)+e^{x} g(x)\)
\(\Rightarrow f^{\prime}(0)=e^{0} \cdot g^{\prime}(0)+e^{0} g(0) \)
\( =1 \cdot 1+1 \cdot 2 \)
\( \left[\because\left\{g^{\prime}(0)=1 \text { and } g(0)=2\right\}\right] \)
\( =1+2=3\)
\(\Rightarrow f^{\prime}(0)=e^{0} \cdot g^{\prime}(0)+e^{0} g(0) \)
\( =1 \cdot 1+1 \cdot 2 \)
\( \left[\because\left\{g^{\prime}(0)=1 \text { and } g(0)=2\right\}\right] \)
\( =1+2=3\)
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