# 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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Question 2 Parts A, B, and C help_outlineImage Transcriptionclose2. 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 fullscreen
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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
Step 2

To find the interval for increasing or decreasing of a function find the first order derivative help_outlineImage Transcriptionclose(x)=x*e* use the product rule d (e) + e* =xe +e 4(x) =xe (x+4) d f'(x)=x)() fullscreen
Step 3

F(x) is increasing when ... help_outlineImage Transcriptionclosef(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, ) fullscreen

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