What is minimum value of e^2x+ e^-2x

Question

Thx

Answer 1

recall that this is just 2 cosh(x).

d/dx (cosh x) = sinh(x)
sinh(x) = 0 at x=0

so, the minimum value is 1+1 = 2

(or 2cosh(0) = 2)

Or, if you insist on the hard way,

y' = 2e^2x - 2e^-2x
= 2e^-2x (e^4x - 1)
y'=0 at e^4x=1, or x=0.