Determine the point(s) of inflection in the equation

[richievuong]

I don't know if I'm posting in the wrong section, because I'm doing this intoductory calculus at high school level:

Anyways here's my question:

Determine the point(s) of inflection in the equation:

y = e^x + e^-x

I know that you have to find y'' and isolate for x to find point(s) of inflection.

My work (sorry if its a pain to read, I don't know how to use latex)

y=e^x + e^-x

y' = [ (e^x)(x) ] + [ (e^-x)(-x) ]

y'' = [ (e^x)(x)(1) ] + [ (e^-x)(-x)(-1) ]
y'' = (e^x)(x) + (e^-x)(x)
y'' = x(e^x + e^-x)

I'm stuck here.

 

[HallsofIvy]

I don't know if I'm posting in the wrong section, because I'm doing this intoductory calculus at high school level:

Anyways here's my question:

Determine the point(s) of inflection in the equation:

y = e^x + e^-x

I know that you have to find y'' and isolate for x to find point(s) of inflection.

My work (sorry if its a pain to read, I don't know how to use latex)

y=e^x + e^-x

y' = [ (e^x)(x) ] + [ (e^-x)(-x) ]

No! The derivative of e^x is e^x, not "(e^x)(x)". The derivative of e^(-x) is -e^(-x) not "e^(-x)(-x)".

y'' = [ (e^x)(x)(1) ] + [ (e^-x)(-x)(-1) ]
y'' = (e^x)(x) + (e^-x)(x)
y'' = x(e^x + e^-x)

I'm stuck here.

 

[richievuong]

Whoops i got confused, I thought derivative of e^f(x) was [e^f(x)] x f(x)

thanks

 

[Office_Shredder]

it's e^f(x)*f '(x)