WeBWorK 6 (3.5-3.8) and assignment

WRITTEN ASSIGNMENT 7: GRAPHING

CALCULUS I, FALL 2022 MATH 1210-090

INSTRUCTOR: WILL FELDMAN

Name: uID:

Problem 1. Consider the function

f(x) = 1

12 x3 − x− 1.

Answer the following questions and use your answers to sketch an accurate graph of f(x). No need to use a calculator!

(a) Find f ′(x).

(b) Find the critical points of f .

(c) Find the interval(s) on which f is increasing and the interval(s) on which f is decreasing.

1

2 CALCULUS I, FALL 2022 MATH 1210-090 INSTRUCTOR: WILL FELDMAN

(d) Find f ′′(x).

(e) Find the interval(s) on which f is concave up and the interval(s) on which f is concave down.

(f) Find any inflection points of f .

(g) Finally, use the previous information to sketch the graph of the func- tion, marking the critical points with a small circle and inflection points of f with a small cross. (Make sure to evaluate the function at least at the critical points and inflection points to place them accurately)

x

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