1. Increasing and Decreasing Functions
Rizzi – Calc BC

2. No time in the given interval
Ap Problem
Given the position equation x(t) = sin(t)+ 2, at what time(s) on [0,2π] will the instantaneous velocity equal its average velocity? A B C D E
t=0
t=π
t=0, π
t=π/2, 3π/2
No time in the given interval

3. Intervals of Increasing/Decreasing
Increasing on: (-3, 0) U (2, ∞) Decreasing on: (- ∞, -3) U (0, 2)

4. Try it – Intervals of Increasing/Decreasing
Determine the open intervals on which 𝒇 𝒙 = 𝒙 𝟑 − 𝟑 𝟐 𝒙 𝟐 is increasing or decreasing. Step 1: Find the critical numbers. Step 2: Use critical numbers to set up test intervals. Step 3: Test a number from each interval in the derivative function. Step 4: Use the results from this test to determine intervals of increasing and decreasing.

5. 𝒇 𝒙 = 𝒙 𝟑 − 𝟑 𝟐 𝒙 𝟐
Increasing: Decreasing:

6. First Derivative Test
Used to determine the relative maximums and minimums of a function.

7. Applying First Derivative Test
Find the relative extrema of 𝒇 𝒙 = 𝟏 𝟐 𝒙−𝒔𝒊𝒏𝒙 in the interval (𝟎, 𝟐𝝅)

8. 𝒇 𝒙 = 𝟏 𝟐 𝒙−𝒔𝒊𝒏𝒙
Increasing: Decreasing: