Graph problem

[sage knoll]

1. Do not ping the Moderators, unless someone is breaking the rules.
2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
3. Do not ping other members randomly for help.
4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[normal gazelle]

@cerulean pasture look at 1) the limits at 0 and +oo 2) when is the function increasing ? decreasing ? what are the maxima/minima ?

you should be able to answer this using calculus

this gives you a first rough shape of the function

[cerulean pasture]

Alright

[normal gazelle]

for more precision, you can also look at 1) the local behaviour at zero 2) the second derivative, which gives you the inflexion points (i.e. points where the derivative changes sign)

[cerulean pasture]

Thank you again!