Math 120: Assignment 3 (Due Tues., Sep. 25 at start of class)
Suggested practice problems (from Adams, 6th ed.):
2.1:
2.2:
2.3:
2.4:
3,9,15,17,21,23,31
3,5,11,17,23,25,35,39,43,47,49,53
1,5,9,15,25,29,31,33,43,47
1,13,15,25,29,33,35,39
Problems to hand in:
1. At which points x is the function f (x) = (4 − x2/5 )−5/2 differentiable? Compute its
derivative.
2. At which points t is the function f (t) =
tive.
√
2
√1+t −1
1+t2 +1
3. Let f and g be differentiable functions. Find
and g 0 .
4. Compute
d −2
dx x
d
dx
differentiable? Compute its deriva-
f (g(xf (x)))2 in terms of f , g, f 0 ,
using the definition of the derivative.
5. Find an equation for the tangent line to the graph y =
6. Show that the graphs y = x2 and y =
√1
x
x2 +3
√
x1/3 + x
at x = 1.
intersect at right angles.
7. Consider the functions f1 , f2 , and f3 , defined by
( j
x
x 6= 0
|x|
fj (x) :=
0 x = 0,
j = 1, 2, 3.
Which of them are continuous at x = 0? Which of them are differentiable at x = 0?
1