Analytic Geometry and Calculus, Section 13804, Fall 2009

September 29, 2009 (Homework)

Richard Aron

Analytic Geometry and Calculus, section 13804, Fall 2009

Instructor: Richard Aron

Final topics in Chapter 2 and introducing Chapter 3...which is really the basis for Calculus I! Please try (hard), and please ask if you're not getting it. Thanks.

Instructions

These will be discussed next Tuesday, October 6, 2009

1. Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 500 cm3, the pressure is 200 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?

2. Two people start from the same point. One walks east at 1 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes?

3. Find the linearization L(x) of the function at a = -1. f(x) = x4 + 5x2 L(x) = 4. Find the linear approximation of the function f(x) = √25-x at a = 0 and use it to approximate the numbers √24.9 and √24.99.

L(x) =

5. The graph of f by hand. (Do this on paper. Your instructor may ask you to turn in this graph.) Use your sketch to find the absolute and local maximum and minimum values of f. (If there is not one, enter NONE.) f(x) = 8 - 4x x ≥ 1

6. Sketch the graph of f by hand. (Do this on paper. Your instructor may ask you to turn in this graph.) Use your sketch to find the absolute and local maximum and minimum values of f. (If there is not one, enter NONE.) f(x) = 2x2 0 < x < 6 7. Find the critical numbers of the function. f(x) = x3 + x2 - x

8. Find the critical numbers of the function. f(x) = x3 + 6x2 - 63x

9. Find the critical number of the function. g(t) = | 3t - 1 |

10. Find the critical numbers of the function. (Enter your answers as fractions.) F(x) = x4/5(x - 2)2

11. Find the critical numbers of the function on the interval 0 ≤ θ < 2π. g(θ) = 4 θ - tan(θ)