Math 131 Fall 2008 Study Sheet for Test 3
I may distribute more sample problems. Note that Section 2.8 is
included. This section was covered in Lab 5. Know the derivatives of
the inverse trig functions, p. 222. Also, know implicit differentiation in
general. Study Lab 5.
Sections 3.3-3.6 deal with the shape of a curve, especially local and
absolute extrema and intervals of concavity. Know how the derivative
behaves at “sharp points”. Study Lab 7.
Regular problems and chapter review Plus
2.8 Implicit Differentiation and Derivatives of
the Inverse Trig Functions
Lab 5
Suggested problems:5-15 (odd), 17, 29-37 (odd)
3.1 Linear Approximations and Newton’s Method
1, 2, 6, 21, 24, 32, 36, 41
42
3.2 Indeterminate Forms and L’Hopital’s Rule
A: 1-21 (odd)
B: 23-37 (odd)
A:39, 40
B:41, 42
3.3 Maximum and Minimum Values
9,10, 23, 24, 35, 36, 44
55, 56
3.4 Increasing and Decreasing Functions
2, 6, 11, 12, 16, 25, 35-38, 40
44, 56
3.5 Concavity and the Second Derivative Test
5-8, 9-14, 16, 27, 37-40, 41-43
46
3.6 Curve Sketching
Lab 7
3.7 Optimization
1, 3, 4, 15, 16, 19, 31
42
Sample Problems: Small set of sample problems
focused on 2.8 and 3.3-3.6.
No Calculators
1.
x
dx
d3arcsin
2.
)3cos(arcsin x
dx
d
Calculators Allowed
1. Given the equation
2 2
24 3 2 4 120x x y y
:
(a)Find
dy
dx
(b)Under what conditions on x and/or y is the tangent to the curve
horizontal?
1
