MATH 1252 Arizona State University Math Worksheet hello everyone I need your help in this math assignment you can see the file attachSpecial notes : want i

MATH 1252 Arizona State University Math Worksheet hello everyone I need your help in this math assignment you can see the file attachSpecial notes : want it in word file MATH1252 Homework 4
Due Wednesday 7/29
1. For the following functions, find the intervals of increasing and decreasing.
(a) f (x) = 3×4 + 8×3 ? 18×2 + 5
(b) f (x) =
x+3
x?4
?
(c) f (x) = x 9 ? x2
4
(d) f (x) = (x + 1) 5
(e) f (x) = xex
2 ?3x
2. Find the value(s) of relative extrema if there are any.
(a) f (x) = x4 ? 8×2 + 9
1
x
x2 ?6x+9
x+2
x
(b) f (x) = x2 +
(c) f (x) =
(d) f (x) = 3xe + 2
(e) f (x) =
x2
ln x
3. Find the open intervals where the functions are concave upward or concave
downward. Find any inflection points.
(a) f (x) = 8 ? 6x ? x2
(b) f (x) = ?x(x ? 3)2
(c) f (x) =
?2
x+1
(d) f (x) = 2e?x
2
4. Use the second derivative test to determine the relative extrema. If the
second derivative test gives no information, use the first derivative test
instead.
(a) f (x) = 2×3 ? 4×2 + 2
(b) f (x) = x3
8
5
(c) f (x) = x 3 + x 3
5. Graph each function, considering the domain, critical points, symmetry,
relative extrema, regions where the function is increasing or decreasing,
inflection points, regions where the function is concave upward or concave
downward, intercepts where possible, and asymptotes where applicable.
(a) f (x) = ?x4 + 6×2
(b) f (x) = 16x +
(c) f (x) = x2 e?x
1
x2

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