1. Chapter 2 Review Calculus

2. Given f(x), find f ‘ (x) USE THE QUOTIENT RULE

3. Given f(x), find f ‘ (x)

4. The profit form the sale of a certain computer part is computed according to: What is the marginal profit from the sale of the 100 th unit?

5. Given f(x), find f ‘ (2)

6. Given f(x), find f -1 (x)

7. Find dy/dx of each equation.

8. Given f(x), find the equation of the horizontal tangent to the curve. Horizontal Tangent means it has a slope of 0

9. A weather balloon is rising vertically at 5 meters/sec. An observer is on the ground 300 meters away. How fast is the distance between the observer and the balloon changing when the balloon is 400 meters high? Make Picture

10. The volume of air in a spherical balloon is decreasing at 2π cubic centimeters per second. How fast is the radius of the balloon changing when r = 2 centimeters?

11. Given s(t), find a(1). s(t) is a position function, a(t) is the acceleration.

12. Given f(x), find f -1 (1) (find 2 Examples)

13. If the position function in feet of a particle at t seconds is, find the following. a.) The average velocity of the particle from t = 0 to t = 2 seconds. b.) The velocity when t = 1 c.) The acceleration at t = 2 seconds.

14. Given f(x), find the slope of the curve at the point given.

15. The base of a triangle is increasing at a rate of 2 inches per minute while the height is decreasing at 5 inches per minute. How fast is the area changing when the base is 10 inches and it’s height is 8 inches. The area is decreasing at a rate of 17 inches per minute

16. What is the equation of the tangent line to the curve y = x 4 which is perpendicular to x + 4y = 6.

17. What is the equation of the tangent line to the curve y = 3x 2 which is perpendicular to 2x + y = 8. y = -2x + 8 Perpendicular Slope = ½

18. Find the derivative implicitly: