# How do you find the tangent line approximation to f(x)=e^x near x=0 ?

Sep 24, 2014

We have to find the derivative of $f \left(x\right)$ and the input the x-value into the derivative to find the numeric slope.

$f \left(x\right) = {e}^{x}$

$f \left(0\right) = {e}^{0} = 1$

Point of tangency is $\left(0 , 1\right)$.

Note that we actually use the chain rule to find the derivative of ${e}^{x}$.

$f ' \left(x\right) = {e}^{x} \cdot 1 = {e}^{x}$

$f ' \left(0\right) = {e}^{0} = 1 \implies s l o p e \mathmr{and} m$