OpenStudy (anonymous):

Need help. Need to find the concavity and inflection point of e^x/(8+e^x)

2 years ago
OpenStudy (danjs):

have you started anythign yet?

2 years ago
OpenStudy (anonymous):

I have the second derivative

2 years ago
OpenStudy (danjs):

what are the two derivatives you got

2 years ago
OpenStudy (anonymous):

\[\frac{ 8e ^{x}(8+e ^{x})^{2}-16e ^{2x}(8+e ^{x}) }{(8+e ^{x})^{4} }\] that's what I have for the second derivative

2 years ago
OpenStudy (lochana):

your second derivative is correct. I just did it

2 years ago
OpenStudy (anonymous):

so where do I go from there?

2 years ago
OpenStudy (lochana):

inflections exist where \[f''(x) = 0\]

2 years ago
OpenStudy (lochana):

and there are two types of concavity. concave upward concave downward you need to find them too in your problem

2 years ago
OpenStudy (anonymous):

I just don't know how to solve the second derivative=0 to get the inflection points

2 years ago
OpenStudy (lochana):

okay. can you simplify numerator of second derivative.

2 years ago
OpenStudy (lochana):

you need simplify numerator. there are some term that cancels each other.

2 years ago
OpenStudy (lochana):

and numerator means upper part of a fraction

2 years ago
OpenStudy (anonymous):

you can only cancel one of the (8+e^x) right?

2 years ago
OpenStudy (lochana):

did you get \[f''(x) = \frac{64e^x}{(8+e^e)^3}\]

2 years ago
OpenStudy (lochana):

\[f''(x) = \frac{64e^x}{(8+e^x)^3}\]

2 years ago
OpenStudy (lochana):

is it?

2 years ago
OpenStudy (anonymous):

ya

2 years ago
OpenStudy (lochana):

okay. To find inflection second derivative should be equal to 0 \[\frac{64e^x}{(8+e^x)^3} = 0\]\[64e^x = 0\]

2 years ago
OpenStudy (lochana):

get it?

2 years ago
OpenStudy (anonymous):

yes

2 years ago
OpenStudy (lochana):

if you want a fraction to be equal to zero, you can't forget denominator(down part of fraction)

2 years ago
OpenStudy (lochana):

so this means \[e^x = 0\] and this is the graph of e^x. I will draw it, so that you can understand easily.|dw:1447295142123:dw|

2 years ago