3.3 Rates of change and behavior of graphs  (Page 5/15)

Can the average rate of change of a function be constant?

If a function $f$ is increasing on $(a,b)$ and decreasing on $(b,c),$ then what can be said about the local extremum of $f$ on $(a,c)?$

How are the absolute maximum and minimum similar to and different from the local extrema?

How does the graph of the absolute value function compare to the graph of the quadratic function, $y=x^2,$ in terms of increasing and decreasing intervals?

$f\left(x\right)=4x^2-7$ on $[1,b]$

$g\left(x\right)=2x^2-9$ on $\left[4,b\right]$

$p\left(x\right)=3x+4$ on $[2,2+h]$

$k\left(x\right)=4x-2$ on $[3,3+h]$

$f\left(x\right)=2x^2+1$ on $[x,x+h]$

$g\left(x\right)=3x^2-2$ on $[x,x+h]$

$a\left(t\right)=\frac{1}{t+4}$ on $[9,9+h]$

$b\left(x\right)=\frac{1}{x+3}$ on $[1,1+h]$

$j\left(x\right)=3x^3$ on $[1,1+h]$

$r\left(t\right)=4t^3$ on $[2,2+h]$

$\frac{f\left(x+h\right)-f\left(x\right)}{h}$ given $f\left(x\right)=2x^2-3x$ on $[x,x+h]$

Estimate the average rate of change from $x=1$ to $x=4.$

Estimate the average rate of change from $x=2$ to $x=5.$