Reflection

This week since we have exams, I’ll do a review of some things we learned throughout the year.

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

2.6 Related Rates
+ When solving related rates problems, you must follow the guidelines.
+ Examples:
1) y = squareroot(x)
1. dy/dt = ? x = 4 dx/dt = 3
2. y = squareroot(x)
3. dy/dt = 1/2x^-1/2
4. dy/dt = 1/2(4)^-1/2
= 3/4
2) xy = 4
1. dy/dt = ? x = 8 dx/dt = 10
2. xy = 4
3. xdy/dt + ydx/dt = 0
4. xdy/dt = -10y
= -10y/x

To find an equation of a tangent line, you must take the derivative of the function and plug in the x-value. (If not given a y-value, plug into the original equation to get the y-value.) Then plug the values into point slope which is: y - y1 = m(x - x1)
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)