Reflection

For our 3rd nine weeks exam, we are reviewing chapters 2 and 3 to go over how to solve different types of derivative equations. An explicit function is solved for y, and an implicit is not solved for y. When you take a derivative you must put the notation dy/dx by any variable except for x.
STEPS:
1) Differentiate both sides with respect to x. d_/dx
2) Collect all dy/dx terms on one side, and move the other terms to the other side.
3) Factor out dy/dx.
4) Solve for dy/dx.
5) Simplify, *replace with original equation if possible.**

Examples:

1) x^2 + y^2 = 9
2x + 2ydy/dx = 0
2ydy/dx = -2x
dy/dx = -2x/2y
= -x/y

2) x^3 + y^3 = 64
3x^2 + 3y^2dy/dx = 0
3y^2dy/dx = -3x^2
dy/dx = -3x^2/3y^2
= -x^2/y^2

Section 2.2
Example:
Find the average rate of change of the function over the given interval.
f(t) = 4t +5 [1, 2]
(1, 9) = 4(1) + 5 = 9
(2, 13) = 4(2) + 5 = 13

m = y2 – y1 / x2 – x1
= 13 – 9 / 2 -1
= 4/1
=4