1. Katherine Han Period 3 4-29-03
Linear Approximation
Katherine Han
Period 3

2. Concept of Linear Approximation
Given a certain equation, f(x), try to find the equation of the tangent line.
After finding the equation of the tangent:
Substitute “x” in order to get a linear approximation of “y.”

3. Using Linear Approximation Given f(x)
Step 1: Find a good “x” value that would be easy to work with, that is near the actual value given – this value will be called “a”
Step 2: dx = real value – a
Step 3: dy = f’(a)*dx
Step 4: f(x) = f(a) + dy
Step 5: Compare to the actual value to check to see that it is close

4. Example Problem
Use Linearization to estimate f(1.99) of f(x)=2x3 -4x2+1
Step 1: Choose a nice value close to 1.99 to be your “a”
a = 2
Step 2: dx = real value – a
dx = = -0.01
Step 3: dy=f’(a)*dx = (24-16)*(-.01) = -.08
Step 4: f(1.99)=f(a)+dy=f(2)+dy= =.92
Step 5: Compare to actual value
f(1.99)=2x3 –4x2+1 =

5. Yet Another Example If f(3) =8, f’(3) = -4, then f(3.02) a= 3
dx = 3.02 – 3 = .02
dy = f’(a)*dx
-4*.02 = -.08
f(x) = f(a) + dy
= 8+(-.08) = 7.92