# Answer to Question #1430 in Calculus for Lauren

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>

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

^{}3x/2e

^{x}+ e

^{-x}= e

^{-x}/2 *(3x + 2)

The first derivation of the function is

y' = 3e

^{-x}/2 - e

^{-x}/2 *(3x + 2) = e

^{-x}/2*(3 -3x - 2) = e

^{-x}/2 *(1 - 3x)

y' = 0: x = 1/3

The second derivation of the function is:

y'' = -3e

^{-x}/2 - e

^{-x}(1 - 3x)/2 = e

^{-x}/2 *(-3 - 1 + 3x) = e

^{-x}/2 *(- 4 + 3x)

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.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment