Course CodeAPPM 1345
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APPM 1345 Exam 1 Spring 2016
INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Credit is
awarded for reasoning; therefore describe all your answers with legible and orderly ex-
planations, and BOX your ﬁnal answers.
1. Consider the function y=x−a2
x2−5and its graph.
(a) (3 points) If a= 5 then what is the domain of y?
(b) (5 points) If a= 0 then demonstrate why yis a decreasing function.
(c) (6 points) If a=4
√5, then describe any domain restrictions as asymptotes, holes,
or jump discontinuities.
(d) (5 points) If yhas a y-intercept at 2, then what must the value of abe?
2. Consider the function f(x) = x4−4x3+ 10
(a) (6 points) Name the relative extrema of f(x).
(b) (6 points) Name any points of inﬂection for f(x).
3. Each of the following problems are not related:
(a) (6 points) Name the critical points of sin(cos x) on [0,2π]
(b) (4 points) Name the general anti-derivative of y=x·x3
(c) (9 points) If pand qare integers and f(x) = (x−1)p(x+ 1)qfor p≥2 and
q≥2, then fhas three critical numbers; name them.
4. (8 points) Use Newton’s Method to estimate a root of x3−4x+ 4 = 0. Start with
an initial guess of x0= 1. Find x2and x101.
CONTINUED ON THE BACK
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