Analyzing Graphs with the First Derivative
Learning Objectives
- Intervals of increasing/decreasing
- Local extrema
- Applications
Exercises
1.
\(f(x)\) is increasing on \((-\infty,4).\)
\(f(x)\) is decreasing on \((4,\infty).\)
\(f(x)\) is decreasing on \((4,\infty).\)
2.
- \(x=-2,0,6\)
- \(x=-\sqrt{27},0,\sqrt{27}\)
3.
Critical Values: \(x=1,3\)
\(f\) is increasing on \((-\infty,1)\) and \((3,\infty).\)
\(f\) is decreasing on \((1,3).\)
Local Maximum of 6 at \(x=1.\)
Local Minimum of 2 at \(x=3.\)
\(f\) is increasing on \((-\infty,1)\) and \((3,\infty).\)
\(f\) is decreasing on \((1,3).\)
Local Maximum of 6 at \(x=1.\)
Local Minimum of 2 at \(x=3.\)
4.
The revenue function is increasing on the interval \((0,140)\) and decreasing on the interval \((140,\infty)\). It has a local maximum of \(\$3920\) when \(x=140\) web cameras are sold.