2. The first derivative shows you the:
• Maximums
• Minimums
• The graph is increasing
• The graph is decreasing
3. Rules
• F’(x)=0 a possible Maximum or minimum
occurs
• F’(x)>0 the graph is increasing; there is a
positive slope
• F’(x)< 0 the graph is decreasing; there is a
negative slope
4. Maximums and Minimums
• Maximums occur when the original graph is
increasing on the left side of the function and
decreasing on the right side of the function.
• Minimums occur when the original graph is
decreasing on the left side of the function and
increasing of the right side of the function.
5. Step 1
• In order to find the maximums and minimums
using the graph of the 1st derivative you set
the f’(x) equation equal to 0. Then you solve
for x
• Example:
6. Step 2
• In order to test to see whether the point is a
maximum or minimum you set up a number
line and test points on both sides of the
number.
- +
I
0 3 5
7. Step 3
• Write it out
F(x) is decreasing from (-∞, 3)
F(x) is increasing from (3,∞)
F(x) has a minimum at x=3 (3,1)
