I was wondering how you would approach this question: Estimate $e^x$ at $x = ln(10) + 0.1$, using the method of small increments (i.e. the linearisation method).
Im not sure what to do i made $f(x) = e^x$ and $f'(x) = e^x$ but I'm not sure what i would chose as my $x_0$ and my $x_1$ and why?
Notice that $x=\ln(10)+0.1$ is just a little bit more than $\ln(10)$. So you should find the linearization of $f(x)=e^x$ at $x=\ln(10)$, and then evaluate this at $x=\ln(10)+0.1$.