For y= 3x/2e^(x) + e^(-x) use graphing techniques to find the approximate intervals on which the function is
A)Increasing
B)Decreasing
C)concave up
D)concave down
E) find local extreme values
F)Find inflection points
1
Expert's answer
2011-02-09T08:46:59-0500
3x/2ex + 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.
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