APPM 1350 Exam 1 Spring 2011
INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Write (1) your name,
(2) 1350/EXAM 1, (3) instructor’s name and (4) SPRING 2011 on the front of your bluebook.
Also make a scoring table with room for 5 problems and a total score. Work all problems. Start each
problem on a new page. Box your answers. A correct answer with incorrect or no supporting work
may receive no credit, while an incorrect answer with relevant work may receive partial credit.
— SHOW ALL WORK —
1. (30 pts) Use the limit definition of the derivative to find:
(a) f0(x) given f(x) = px2+ 9
(b) f0(0) given f(x) = 5x4+ 3x+ 20
(c) d2f
dx2given d
dxf(x) = 1
10x+ 6
2. Suppose the position function of a particle in motion is given by s(t)=5t4+ 3t+ 20 ft, where tis in
seconds.
(a) (8 pts) Find the average rate of change of the position of the particle from t= 0 seconds to
t= 2 seconds.
(b) (6 pts) Find the instantaneous rate of change of the position of the particle when t= 0 seconds.
3. (18 pts) Let f(x) = x2+ 1, m(x) = xand b(x) = √x2−1,
(a) Find (f◦m◦b)(x) and state the domain.
(b) Find (f+m)(x) and state the domain.
(c) Find b
m(x) and state the domain.
4. (20 pts) Justify your answers for all the questions below. Consider the function f(x) = 1
x+ 1 +2x
|x|,
does f(x) have any:
(a) vertical asymptotes? If so, what are they?
(b) horizontal asymptotes? If so, what are they?
(c) removable discontinuities? If so, what are they?
(d) jump discontinuities? If so, what are they?
5. (18 pts) Let a, b and cbe constants and consider the function f(x) where
f(x) =
x+ 6, x ≤0
cx2+bx +a, 0<x<1
7x+c, x ≥1
(a) Find all values of a,b and cfor which f(x) will be continuous at x= 0 and x= 1?
(b) For what values of a, b and cwill f(x) be differentiable at x= 0 and x= 1?
(c) Find the equation of the tangent line to f(x) at x=−1.
END