# Math Help - local linearization

1. ## local linearization

Let f(x)=3+cos(2x+(pi/2))

Find the local linearization of the function at the point a=0.

Use your linearization to find and approximation for f(0.4)

2. Originally Posted by thecount
Let f(x)=3+cos(2x+(pi/2))

Find the local linearization of the function at the point a=0.

Use your linearization to find and approximation for f(0.4)

This is the same as finding the tangent line at the point x=0

$f'(x)=-2\sin\left( 2x+ \frac{\pi}{2}\right)$

$f'(0)=-2\sin\left( \frac{\pi}{2}\right)=-2$

note that $f(0)=3$

so the approximation is

$L(x)= -2x+3$

$f(.4) \approx L(.4)=-2(.4)+3=2.2$