- Spinning weight (e.g., person twirling on a swing)
- How does angular speed change with distance to weight?
- How does angular speed change with distance to weight?
- Quarter cone of dirt
- How does cost change with radius when radius = 10 ft?
- dC/dr = 5/27 πr/12
- If r = 10 ft dC/dr = (5 × π × 10) / (27 × 12)
- = (50 × π) / 324
- = 157.08 / 324
- Or about $0.50 / foot
- How does cost change with radius when radius = 10 ft?
- How much more would it cost me to make the dirt cone 0.5 ft bigger in radius?
- 25 cents—dC/dr × 1/2 foot
- Approximate a function by derivative = linearization
- What’s 984
- Round 98 to 100
- 1004 = 100,000,000
- y = x4
- dy/dx = 4x3
- 984 should be about 100,000,000 - 2×4×1003
- = 100,000,000 - 8,000,000
- = 92,000,000
- Really 92,236,816
- Section 4.1
- Example
- y = 4 - x2
- Should have max at x = 0
- dy/dx = -2x
- Solve for x st dy/dx= 0
- x = 0
- Extrema
- Section 4.1
- Mean Value Theorem
- Section 4.2