Question

对于任意实数x≥0,f(x)=ex+ax恒大于零,则实数a取值范围

Answer 1

f(x) =e^x + ax

x≥0,f(x)>0恒成立

e^x + ax >0

a > e^x/x for x≥ 0

let

g(x) = e^x/x

g'(x) = [e^x - xe^x]/x^2

= e^x[1-x]/x^2

g'(x) = 0

=> x =1

g''(1) >0 ( min)

a > g(1) = e

ie a> e