01:640:135 Midterm: 01:640:135 Test Fall 2016Exam
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(10) 1. Suppose f(x)=
. Use the denition of derivative to nd f
(9) 2. Find an equation for the line tangent to the graph of y=
at the point where
(12) 3. Assume that the functions u(x) and v(x) are dened and dierentiable for all real
numbers x. The following data is known about u,v, and their derivatives.
2 3 4 1 2
3 2 1 3 1
4 1 3 0 2
Dene 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:
(14) 4. Suppose that the function f(x)isdescribed by
Ax +Bif 0 x1
if 1 <x
a) Find Aand Bso that f(x)iscontinuous for all numbers. Briey 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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