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

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Answer 1 · 2014-09-24T04:19:59

We have to find the derivative of #f(x)# and the input the x-value into the derivative to find the numeric slope.

#f(x)=e^x#

#f(0)=e^0=1#

Point of tangency is #(0,1)#.

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

#f'(x)=e^x*1=e^x#

#f'(0)=e^0=1 => slope or m#