Reflection

In calculus this week, we finished reviewing and learning about some of chapter 2. We also took a test on chapter 2. In this chapter we learned about derivatives. To help us with the derivatives, we learned how to use the shortcut, and we also learned different direction sets, plus we learned how to find average velocity and other things.

Example: Find an equation of the tangent line to the graph of f at the given point
f(x) = x/x+4, (-5, 5)
= (x+4)(1) -[(x)(1)] / (x+4)^2
= x+4-x / (x+4)^2
= 4/(x+4)^2
m = 4/(-5+4)^2 = 4/1^2 = 4
point slope: y - 5 = 4(x + 5)

Example:
use shortcut
f(x) = x^2
= 2x

Quotient Rule:
f(x)/g(x) = g(x)f’(x) – [f(x)g’(x)] / (g(x))^2
(recopy bottom)(derivative top) – [(recopy top)(derivative bottom)] / (bottom)^2
Example: f(x) = x / x^2 + 1
f’(x) = (x^2 + 1)(1) – [(x)(2x)] / (x^2+1)^2
= x^2 + 1 – 2x^2 / (x^2 + 1)^2
= -x^2 + 1 / (x^2 + 1)^2