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Midterm

# 01:640:135 Midterm: 01:640:135 Test Fall 2016Exam

Department
Mathematics
Course Code
01:640:135
Professor
All
Study Guide
Midterm

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1A
(10) 1. Suppose f(x)=
3
x+2
. Use the denition of derivative to nd f
0
(x).
(9) 2. Find an equation for the line tangent to the graph of y=
4x
2+x
2
at the point where
x=1.
(12) 3. Assume that the functions u(x) and v(x) are dened and dierentiable for all real
numbers x. The following data is known about u,v, and their derivatives.
x u(x)v(x)u
0
(x)v
0
(x)
2 3 4 1 2
3 2 1 3 1
4 1 3 0 2
Dene f(x) = u(x)v(x), g(x) = u(x)=v(x), and h(x) = u(v(x)). Give the values of the
following with a brief indication of how they were obtained:
a) f
0
(2)
b) g
0
(3)
c) h
0
(4)
(14) 4. Suppose that the function f(x)isdescribed by
f(x)=
8
<
:
3x
2
if x<0
Ax +Bif 0 x1
2
x
if 1 <x
:
a) Find Aand Bso that f(x)iscontinuous for all numbers. Briey explain your answer.
b) Sketch y=f(x) on the axes given for the values of Aand Bfound in a) when xis in
the interval [2;2].
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