MATH 1210 PRACTICE PROBLEMS FOR MIDTERM 2
The first 6 questions form a practice exam. Solutions will be provided
in a separate document. The other 6 questions are additional practice
problems.
1. Practice Exam
Problem 1. State the intermediate value theorem.
Problem 2. Classify the discontinuities of the following function:
(1) f(x) =
−x2x < −4
1x=−4
x−1−4< x < 0
x30≤x < 1
2x= 1
x31< x
Problem 3. Let f(x) = (x−43)21 tan(x3). Compute f0(x).
Problem 4. The sum rule for derivatives which you may assume says
that if f1, f2are differentiable then (f1+f2)0=f0
1+f0
2. For n∈N
prove that
(2) ³n
X
k=1
fk´0
=
n
X
k=1
f0
k
when each fkis differentiable.
Problem 5. Consider the equation y3−3xy = 4. Assume that yis a
function of x. Compute dy
dx .
Problem 6. Sketch the graph of f(x) = 3x3−4x. Your sketch will
clearly indicate the points of inflection, the local maxima and minima,
and the intercepts and your work will show how you obtained those
points.
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