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Question 45

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Graph the function and locate intervals on which the function is increasing or decreasing, open

intervals on which the function is concave up or concave down, and all inflection points.

f(x)=x4 ex

+++

f is increasing on (-, -4] and [0,-)

and decreasing on [-4, 0]. f is concave

up on (-2, and concave down on

(-∞, -2). f has an inflection point at x = -2

f is increasing on [-4, 0] and decreasing

on (-, -4] and [0.). f is concave up on

(-6, -2) and concave down on (-09-6) and

(-2,-). f has inflection points at x = -6

and x = -2.

+++++

-10 -8

f is increasing on [0, 4] and decreasing

on (-∞, 0] and [4, *). f is concave up on

(-092) and (6, and concave down on

(2,6). f has inflection points at x = 2

and x = 6.

f is increasing on (-, -4] and [0,-)

and decreasing on [-4, 0]. f is concave

up on (-09-6) and (-2, od and concave

down on (-6, -2) f has inflection points

at x = -6 and x = -2.

Fig: 1