165 Math Discussion (3.1-3.2) Tuesday 10/02/2006 The Quiz#5 will be similar to these exercises or these examples in the book: Examples 3.1.1, 3.1.3; Examples 3.2.1, 3.2.3. 1. Find the intervals of increase and decrease for the given function.
9 F (x) = x + x .
2. Given a function f (x) = 3x4 - 8x3 + 6x2 + 2. (a) determine the critical numbers1 , and the critical points. (b) classify each critical point as a relative maximum, a relative minimum, or neither.
3. Same as the previous problem, given f (x) =
t . t2 +3
4. Given f (x) = x(2x + 1)2 . (a) Determine the intervals where the graph is concave up or concave down. (b) Find the coordinates of all inflection points2 .
5. Given f (x) = x4 - 4x3 + 10. (a) Find the relative maxima and relative minima. (b) Find the inflection points.
6. as Same the previous problem, given f (x) = (x2 - 5)3 .
1 2
A number c in the domain of f (x) is called a critical number if either f (c)=0 or f (c) does not exist. An inflection point is a point on the graph of a function where the concavity changes
Math 165 QUIZ#5 NAME: Closed book. No discussion. Receiving or giving aid is a cause for this quiz to be graded as zero point. 1. Find the intervals of increase and decrease for the function f (x) = 2x3 + 3x2 ...