- #1
sutupidmath
- 1,630
- 4
i am having some difficulties in proving that
y=chx=(e^x+e^(-x))/2 is decreasing in the interval (- infinity,0) and increasing in (0, infinity)
i know that a function is increasing in (a,b) if for two variables from that interval let's say x' and x" that are related x'<x" than f(x')<f(x"), sot at this case f is increasing in (a,b).
if x'<x", but f(x')>f(x"), than f is decreasing in (a,b).
here is what i did with chx:
x'<x", x',x">0 , then from the monototy of exponential functions we know that e^x'<e^x" and ( 1/e^x")<(1/e^x')..
here is where i get stuck..
any help?
y=chx=(e^x+e^(-x))/2 is decreasing in the interval (- infinity,0) and increasing in (0, infinity)
i know that a function is increasing in (a,b) if for two variables from that interval let's say x' and x" that are related x'<x" than f(x')<f(x"), sot at this case f is increasing in (a,b).
if x'<x", but f(x')>f(x"), than f is decreasing in (a,b).
here is what i did with chx:
x'<x", x',x">0 , then from the monototy of exponential functions we know that e^x'<e^x" and ( 1/e^x")<(1/e^x')..
here is where i get stuck..
any help?