Given a function 
and a point 
, the linear function
is called the first-order Taylor polynomial of about . (Note that this is an equation for the tangent line to the graph of 
at the point .) Determine 
for the function 
T_1(x)=
+23246 The derivative of e^(18.4x) = e^(18.4x) · 18.4 = 18.4e^(18.4x)
f(11.2) = e^(18.4 · 11.2) = e^(206.08)
f'(11.2) = 18.4e^(18.4 · 11.2) = 18.4e^(206.08)
T1(x) = e^(206.08) + 18.4e^(206.08) · (x - 11.2)
Use can use a calculator to get a decimal approximation for f(11.2) and f'(11.2).
+23246 The derivative of e^(18.4x) = e^(18.4x) · 18.4 = 18.4e^(18.4x)
f(11.2) = e^(18.4 · 11.2) = e^(206.08)
f'(11.2) = 18.4e^(18.4 · 11.2) = 18.4e^(206.08)
T1(x) = e^(206.08) + 18.4e^(206.08) · (x - 11.2)
Use can use a calculator to get a decimal approximation for f(11.2) and f'(11.2).
