2. Given f(x) = x4ea. Find the intervals where f(x) is increasing or decreasing, and the pointswhere local extrema occur, if anyb. Find the intervals where f(x) is concave up or down, and the inflectionpoints if any.c. Find the horizontal and vertical asymptotes, ifd. Sketch the graph of f(x).any.3. Find the vertical and horizontal asymptotes of the following functions, if any1b. g(x)1sin xXc. h(x) =a. f(x11e - 1In xHI8

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Asked Nov 8, 2019
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Question 2 Parts A, B, and C

2. Given f(x) = x4e
a. Find the intervals where f(x) is increasing or decreasing, and the points
where local extrema occur, if any
b. Find the intervals where f(x) is concave up or down, and the inflection
points if any.
c. Find the horizontal and vertical asymptotes, if
d. Sketch the graph of f(x).
any.
3. Find the vertical and horizontal asymptotes of the following functions, if any
1
b. g(x)
1
sin x
X
c. h(x) =
a. f(x
11
e - 1
In x
HI8
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2. Given f(x) = x4e a. Find the intervals where f(x) is increasing or decreasing, and the points where local extrema occur, if any b. Find the intervals where f(x) is concave up or down, and the inflection points if any. c. Find the horizontal and vertical asymptotes, if d. Sketch the graph of f(x). any. 3. Find the vertical and horizontal asymptotes of the following functions, if any 1 b. g(x) 1 sin x X c. h(x) = a. f(x 11 e - 1 In x HI8

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Expert Answer

Step 1

For the given function find

  1. Interval where the function is increasing or decreasing
  2. Interval where the function is concave up or concave down, point of inflection if any
  3. Vertical and Horizontal asymptotes if any
f(x)xe
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f(x)xe

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Step 2

To find the interval for increasing or decreasing of a function find the first order derivative

(x)=x*e*
use the product rule
d
(e) + e*
=xe +e 4(x)
=xe (x+4)
d
f'(x)=x)()
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(x)=x*e* use the product rule d (e) + e* =xe +e 4(x) =xe (x+4) d f'(x)=x)()

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Step 3

F(x) is increasing when ...

f(x)> 0
xe (x+4)>0
e >0
x(x+4)>0
Whenx < O
x + 4 <0
x <-4
(-4)
Whenx >0
x + 40
x >-4
(0,or)
f(x)isincreasin g in(-r,-4)U(0, )
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f(x)> 0 xe (x+4)>0 e >0 x(x+4)>0 Whenx < O x + 4 <0 x <-4 (-4) Whenx >0 x + 40 x >-4 (0,or) f(x)isincreasin g in(-r,-4)U(0, )

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Tagged in

Math

Calculus

Functions