CPM Homework Help : AC Problem 9-81

Mathematics is full of all kinds of different functions, but it is comforting to know that some things remain constant for all of them. For example, to the slope of the at $x=2$ , the same procedure, regardless of the function. For each of the following functions, formula for to

Hint:

$m=\frac{f(2+h)-f(2)}{h}$

$f(x)=2x^2$
Step (a):
$m=\frac{2(2+h)^{2}-f(2)}{h}$

$f(x)=3^x$
Step (b):
$m=\frac{3^{(2+h)}-3^{2}}{h}$

$f(x)=\log(x)$
Step (c):
$m=\frac{\log (2+h)-\log(2)}{h}$

$f(x)=\cos(x)$ ( $x$ in radians)
Step (d):
$m=\frac{\cos(2+h)-\cos(2)}{h}$ Use the eTool below to help you with this problem.