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Question: Answered & Verified by Expert
If $f(x)=b \cdot e^{a x}+a \cdot e^{b x}$, then $f^{\prime \prime}(0)=$
MathematicsDifferentiationMHT CETMHT CET 2022 (10 Aug Shift 1)
Options:
  • A $(a+b)$
  • B $a b(a+b)^2$
  • C $2 a b(a+b)$
  • D $a b(a+b)$
Solution:
2225 Upvotes Verified Answer
The correct answer is: $a b(a+b)$
$\begin{aligned} & f(x)=b \cdot e^{a x}+a \cdot e^{b x} \\ & \Rightarrow f^{\prime}(x)=b a e^{a x}+a b e^{b x} \\ & \Rightarrow f^{\prime \prime}(x)=b a^2 e^{a x}+a b^2 e^{b x} \\ & \Rightarrow f^{\prime \prime}(0)=b a^2+a b^2=a b(a+b)\end{aligned}$

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