Math 151 WIR 9, Spring Semester 2015
© Dr. Rosanna Pearlstein
Sections 5.1, 5.2, 5.3, 5.5.
1. The graph of the second derivative f " of function f is shown below
a) For what value(s) of x does f ' have a local maximum or minimum?
b) For what value(s) of x is the graph of f concave up?
c) For what value(s) of x is the graph of f concave down?
d) Where are the points of inflection of the graph of f located?
2. Find the following limits:
a. lim𝑥→+∞
lnx
𝑒𝑥
b. lim𝑥→+∞ √𝑥 2 − 6𝑥 − 𝑥
𝑥+𝑐𝑜𝑠𝑥
c. lim𝑥→+∞ 𝑥+𝑠𝑖𝑛𝑥
3. Find the absolute maximum and absolute minimum values of f on the given interval.
𝑓(𝑥) = 𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 in [0, 2𝜋].
Math 151 WIR 9, Spring Semester 2015
© Dr. Rosanna Pearlstein
4. Do all the necessary math to sketch the graph of 𝑓(𝑥) = 𝑥𝑒 −𝑥 .
5. Find the absolute maximum value and the absolute minimum value attained by
1
𝑓(𝑥) = 𝑥(1−𝑥) in the interval [2,3].
6. Do all the necessary math to sketch the graph of 𝑓(𝑥) = 𝑥 2 +
16
𝑥
.
7. Find the absolute maximum value and the absolute minimum value attained by
𝑓(𝑥) = 𝑥1/2 + 𝑥 3/2 in the interval [0,4].
8. What angle
between two edges of length 3 will result in an isosceles triangle with the
largest area? (See diagram.)
9. A cylindrical can is made to hold 1 liter of oil. Find the dimensions of the can that will
minimize the cost of the metal to manufacture the can.
10. Find all points on the curve 𝑥 2 − 𝑦 2 = 1 that are closest to the point (0, 2).