Sections 5.1, 5.2, 5.3, 5.5.

```Math 151 WIR 9, Spring Semester 2015
&copy; Dr. Rosanna Pearlstein
Sections 5.1, 5.2, 5.3, 5.5.
1. The graph of the second derivative f &quot; 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. limπ₯→+∞
lnx
ππ₯
b. limπ₯→+∞ √π₯ 2 − 6π₯ − π₯
π₯+πππ π₯
c. limπ₯→+∞ π₯+π πππ₯
3. Find the absolute maximum and absolute minimum values of f on the given interval.
π(π₯) = π πππ₯ + πππ π₯ in [0, 2π].
Math 151 WIR 9, Spring Semester 2015
&copy; Dr. Rosanna Pearlstein
4. Do all the necessary math to sketch the graph of π(π₯) = π₯π −π₯ .
5. Find the absolute maximum value and the absolute minimum value attained by
1
π(π₯) = π₯(1−π₯) in the interval [2,3].
6. Do all the necessary math to sketch the graph of π(π₯) = π₯ 2 +
16
π₯
.
7. Find the absolute maximum value and the absolute minimum value attained by
π(π₯) = π₯1/2 + π₯ 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 π₯ 2 − π¦ 2 = 1 that are closest to the point (0, 2).
```