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
x
3 − 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
0
(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
00(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 function, 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
y
