Announcements
Quizes were okay. Mostly good. Grade available online but not handing back quite yet because others still have to take Them.
FRESHMAN’S DREAM \((x+2)^2\neq x^2 + 2^2\)
\(3^2 = 9 \neq 1^2 + 2^2 = 5\)
Rates of change and behaivors of graphs
Rate of change describes how the output quantity changes in relation to input quantity.
Miles per hour should be the best. How the miles traveled changes per hour.
What makes the difference between linear and exponential equations.
RELATE THINGS TO A LINEAR
Average rate of change
\(ARoT = \frac{Change of output}{change of input} = \frac{\delta y}{\delta x}\)
\(=\frac{f(b) - f(a)}{b-a}\)
Increasing/decreasing functions
A function is increasing if \(f(b) - f(a) > 0\), decreasing if \(<0\), constant if \(=\). Average
| function | avg RoC | formula |
|---|---|---|
| increasing | positive | \(f(b) > f(a)\) |
| decreasing | negative | \(f(b) < f(a)\) |
Local Extrema
Maximum Point where change from increasing to decreasing Minimum Point where change from decreasing to increasing
Concavity
Concave down vs concave up
Concave Up means ARC is slowing Concave Down means ARC is increasing
Inflection point:
Where a function changes from concave down to concave up.
Examples
TEXTBOOK HAS BUNCH OF EXAMPLES of functions page 46