Question

设a>0,f(x)=(e^x)/a+a/(e^x)是R上的增函数.

Answer 1

(1)

f(x)=(e^x)/a+a/(e^x)

f'(x) = (e^x)/a - a/(e^x)

f(x)是R上的增函数

then f'(x)≥0

=>(e^x)/a - a/(e^x)≥0

(e^2x - a^2)/ae^x ≥0

(e^2x - a^2)≥0

e^2x≥a^2

2x≥2lna

x≥lna

a ≤ e^x #

(2)

f'(x)=0

=>x=lna