Math 160
Exam 2
Fall 1999
- (48 pt) Find the derivatives of the following functions:
a)
b)
c)
d)
e)
![](Image128.gif)
is differentiable.
f)
g)
h)![](Image609.gif)
- (10 pt) Find the tangent line to the curve given by
at the point (-2,-1).
- (8 pt) Use linear approximations to estimate the value of
.
- (12 pt) Consider the function
. Find all critical numbers and determine which (if any) are local extreme values.
- (6 pt) Show that the radius of any circle is always perpendicular to its tangent line at that point.
- (6 pt) Show that for any value of
, the polynomial
has one and only one root.
- (15 pt) Two cars leave an intersection at the same time. The first car travels due north at 60 miles per hour and the second car travels at an angle 30°
south of east at 45 miles per hour. How fast is the distance between the cars changing after 2 hours?
- (5 pt) Show that any function of the form
satisfies the equation ![](Image615.gif)