# Chapter 4 - Curve Sketching

Chapter 4.1 - Increasing and Decreasing Functions

1. 2.

Find constants a, b, c and d such that the graph of f(x) = ax^3 + bx^2 n+ cx + d will increase to the point (1,12), decrease to the point (4, -15) and then continue increasing.

Answer:  a = 2, b = -15, c = 24, d = 1

Chapter 4.2 - Critical Points, Local Maxima, and Local Minima

3. 4. Graph the curve f(x) = 0.1 x^3 + 0.3 x^2 - 2.4x + 2 by finding maximum and minimum points and intercepts if possible.

5.     For each of the following, you are given a graph of y = f(x), and your job is to graph y = f '(x)

a) b) c) 6. Chapter 4.3 - Vertical and Horizontal Asymptotes

7. 8.

9. abc 10. ab 11. Chapter 4.4 - Concavity and Points of Inflection

12 13 14 15.     Find constants a, b and c such that the function y = a x^3 + b x^2 + cx has a point of inflection at (-2, 88) and a local minimum at (2, -40).

Answer:  a = 1, b = 6, c = -36

Chapter 4.5 - An Algorithm for Curve Sketching

16.    Graph y = x^3 - 7x^2 + 15x - 9

17. 18. 19. 20. 21. 22. 23. 