How do you find the linearization at a=0 of #f(x) = e^(5 x)#?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Nov 29, 2015
Linearization uses the Linear Approximation Method.
#f_T(a) = f(a) + f'(a)(x-a)#
So, let's take the derivative first, since that's one thing we don't have. If we let
Finally, let's plug in
#f_T(0) = f(0) + f'(0)*(x)#
#= e^0 + 5*e^0*(x)#
#= 5x + 1#
So the tangent line is just
