Answered: TUTORIAL 35 Given a function f(x) = 2x… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 8E

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Question

35.no 1 do like example 3 solution

4
Example 3: Find the interval of x where the function f(x ) = x + 3x
is increasing or decreasing.
Solution:
f'(x) =
3x + 6x
Critical values
-2,0
%3D
Sign of: 3x + 6x
Interval
Test Value
+ve
(-0,-2)
(-2,0)
- 1
-ve
(0, 0)
+ve
2
f (x) decreasing, f'(x) < 0 = f(x) decreasing in the interval (-2,0)
f (x) increasing,
f'(x) > 0 = f (x) increasing in the interval (-0,-2)U(0,0)
f(x) = x + 3x? - 4
f (x)
Increasing (-o,-2),
Increasing (0,)
Decreasing (-2,0)

2x - 5x is a decreasing function in the interval (-1, 5).
7. Find the interval where f (x) is increasing
TUTORIAL 35
12x - 5. Find the intervals where
Given a function f(x) = 2x +3x
1(x) is increasing and decreasing.
2.
Given f(x) = 4x + 15x- 18x
3.
Show that f(x) =
Given the function f(x) = (x + 1)(x - 2).
Find the interval where f(x) is increasing and decreasing.
5x
Given the function f(x) =
5.
Find the interval where f (x) is increasing or decreasing.
6.
Given the function f(x) =
1 + x
Find the interval where f(x) is increasing or decreasing.
Given the function f (x) =
X - 4
Find the interval where f (x) is increasing or decreasing.
8.
Given the function f (x)
X- 2
X + 2
Find the interval where f(x) is increasing or decreasing.
Answers:
Increasing (-,-2) U (1,)
Decreasing : (-2,1)
1.
Increasing : (-, -3) u (5.)
Increasing: (-,0) u (2,)
Decreasing: (0,2)
5.
2.
4.
Decreasing: (-, 2) u (2,)
Increasing: (-,-1) U (-1, )
Decreasing: (-«, 4) U (4.)
Increasing: (-,-2) (-2, )

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