Curve Sketching

Table Of Contents

Increasing and Decreasing Intervals

Increasing

function is increasing on an interval if $f(x_1)<f(x_2)$ Derivative must be positive $f^{\prime }(x)>0$

Decreasing

function is decreasing on an interval if $f(x_1)>f(x_2)$ Derivative must be negative $f^{\prime }(x)<0$

Chart Method

1. Find critical values
2. Make a table of intervals between each critical value
3. Sub in values into the f’(x) function for each interval and see if positive or negative