1. Calculus 3-4
Rates of Change

2. Instantaneous Rate of Change
𝑓 ′ 𝑥 The derivative at a given point will tell you the instantaneous rate of change (slope) at that point

3. 𝐴=𝜋 𝑟 2 Find 𝑑𝐴 𝑑𝑟 when 𝑟=2, 𝑎𝑛𝑑 𝑟=5 𝑑𝐴 𝑑𝑟 =2𝜋𝑟 𝑟=2: 𝑑𝐴 𝑑𝑟 =4𝜋
𝑟=2: 𝑑𝐴 𝑑𝑟 =4𝜋
𝑟=5: 𝑑𝐴 𝑑𝑟 =10𝜋
Why is 𝑑𝐴 𝑑𝑟 larger at 𝑟=5
As the radius increase the rate that the area of circle increase as well

4. Linear Motion
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦= 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ′ 𝑠 𝑡 =4 𝑥 2 +8𝑥−9 𝑣 𝑡 =8𝑥+8

6. Motion under Gravity
𝑠 𝑡 = 𝑠 0 + 𝑣 0 𝑡− 1 2 𝑔 𝑡 2 𝑣 𝑡 = 𝑑𝑠 𝑑𝑡 = 𝑣 0 −𝑔𝑡 𝑔≈9.8 𝑚 𝑠 2 𝑜𝑟 32 𝑓𝑡 𝑠 2

7. Find the velocity of an object dropped from a height of 300 m at the moment it his the ground.
Equation for the object
How long before it hits the ground
Velocity function
Velocity at that time

8. 𝑠 𝑡 =300− 𝑡 2
𝑡= 𝑠𝑒𝑐𝑠 𝑣 𝑡 =−9.8𝑡 𝑣 0 =− 𝑚/𝑠

9. Problems
3.4 #1, 7, 9-11, odd NOT 23 and 29, 38, and 49