Please help me ASAP

Question

It's about sketching the graph based on precalculus and calculus.

draw the graph y=(1+e^x)^-2

When I tried to first derivative test, I couldn't see at any point that makes 'f'(x)=0'

Does it right? I tried to find where is increasing and decreasing but I can't find it.

Please help me.

Answer 1

use a graphing calculator handheld or on line, such as desmos

it's an everywhere decreasing function

with y intercept (0,1/4) and horizontal asymptote y=0 or the x axis

Answer 2

That's correct! Setting f'(x)=0 gives you no solution. This must mean the function is either always increasing or decreasing because there is no "turning point" where the function will switch from increasing to decreasing or decreasing to increasing. I would recommend plugging in some points to see which of these it will be. Hope this helps!