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The answer to the question is one of the below

The answer to the question is one of the below-example-1
User Wakim
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1 Answer

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The linearization of a function at first order is given by:


f(x+\Delta x)=f(x)+f^(\prime)(x)*\Delta x\ldots(A)

where f'(x) denotes the derivative of f(x). In our case,


\begin{gathered} f(x)=e^x \\ \text{then} \\ f^(\prime)(x)=(de^x)/(dx)=e^x \end{gathered}

Then, by substituting this result into equatio (A), we get


f(x+\Delta x)=e^x+e^x*\Delta x

or equivalently


f(x+\Delta x)=e^x+\Delta xe^x

Therefore, the answer is the first option.

User Leishman
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