Using ANY method (other than computer), find dy/dx in problems 1 - 6.

1.

2.

Let:

3.

or

4.

5.

or

6.

Show all work in problems 7 - 10.

7. Text problem 64, page 162

x = # of people
p = fare

No Load Price

Max Load Price

Revenue:

Max Revenue at $4 fare resulting in 40 riders and a max revenue of $160.

solve:

8. Text problem 82, page 163

find tangent at (1,2)

tangent line equation:

9. Text problem 84, page 163

Volume formula (for this can):

Comparing an exact change in volume vs. an estimated volume

Let:

Example

first (exact) derivative at r₀:

direct calculation of deltaV

estimated difference:

Volume diff erence (error) depends upon r and dr.

dV increases linearly as r_o increases.

10. Text problem 86, page 163

given: a = 15 feet +/- one inch.

Calculate h and estimate the error in the estimate

Let:

by observation:

or

Linearize estimate:

Computed: