We have the function $$f:\mathbb{R}\rightarrow \mathbb{R} \\ f(x)=\frac{x+1}{e^x}$$
I want to draw the graph of the function.
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I have calculated the following :
The first derivative is $f'(x)=\frac{-x}{e^x}$ and the second derivative is $f''(x)=\frac{x-1}{e^x}$.
We have that at $x=0$ there is a local maximum.
As for the asymptotic behaviour we have that $\displaystyle{\lim_{x\rightarrow +\infty}f(x)=0}$ and $\displaystyle{\lim_{x\rightarrow -\infty}f(x)=-\infty}$.
What else do we need to draw the graph ? Do we maybe need also the intersection with the $x$-axis and with the $y$-axis ?
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EDIT:
I have done the following :
Is that correct? Do we get this from each given information?
How do we see the convexity in each interval ?
It truly depends on how accurate you want to be. But a good idea would be to first make points at all the numerical values, for example at $x=1$ you make a point with the height $3/e^2$. You can then do this again but with all the values that are in-between two numerical values,for example at $x=1.5$, you can keep doing this until you have a satisfying amount of points, then you can draw a line between the points!
Example of drawing points and then drawing lines between the points