proofs question (1 Viewer)

[poptarts12345]

let f(x) = e^x -x -1

a) prove f(x) > 0 for all x except 0
b) by finding a suitable value of x, prove e^(pi) > (pi)^e

i know how to do question a; but how do you get question b? for question b, the answer says substitute x= (pi/e) - 1; but how do you find this value in the first place?

 

[stupid_girl]

You can do it in reverse (from bottom to top).

f(pi/e -1)>f(0)
e^(pi/e -1)-(pi/e -1)+1>0
e^(pi/e -1)>pi/e
e^(pi/e)>pi
pi/e>ln pi
pi ln e>e ln pi
e^pi>pi^e