Question #1430

For y= 3x/2e^(x) + e^(-x) use graphing techniques to find the approximate intervals on which the function is <br>
A)Increasing<br>
B)Decreasing<br>
C)concave up<br>
D)concave down<br>
E) find local extreme values<br>
F)Find inflection points<br>

Expert's answer

The first derivation of the function is

y' = 3e

y' = 0: x = 1/3

The second derivation of the function is:

y'' = -3e

y'' = 0: x = 3/4

The fustion increases on the (-inf, 1/3) and decreases on (1/3, inf)

The local extreme is x= 1/3;

The fuction concaves up on (-inf, 3/4), concaves down on (3/4, inf)

The inflection point is 3/4.

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