4.1: Linear Approximation and Applications

Linear Approximation is easy to understand,
but I still find calculus to be fairly bland.
I prefer Approximation to Linearization,
but I'd still rather enjoy summer vacation.


Problem:

Find the linearization of f(x)=cos(x) + 3x^(5/2), when x=11. Then find the linear approximation at x=12.

f'(x)=-sin(x)+ (15/2)x^(3/2)
f'(11)=-sin(11) + (15/2)x^(3/2)=274.61

f(11)= cos(11) + 3(11)^(5/2)=12.03.94

L(x)=f'(11)(x-11)+f(11)

at x=12...

f(12)=f'(11)(12-11)+f(11)
f(12)=(274.61)(1)+(1203.94)
f(12)=1478.55