Which quadrants and axes does $f (x) = - x e^{x}$ $f(x)=-xe^x$ pass through?

Question

1533 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-04T11:05:10

$f (x)$ $f(x)$ runs through Q2 and Q4, intersecting both axes at $(0, 0)$ $(0, 0)$ .

Given:

$f (x) = - x e^{x}$ $f(x) = -xe^x$

Note that:

$e^{x} > 0$ $e^x > 0" "$ for all real values of $x$ $x$
Multiplying $y$ $y$ by any positive value does not change the quadrant in which $(x, y)$ $(x, y)$ lies, or any axis on which it lies.

So the quadrant/axes behaviour of $f (x) = - x e^{x}$ $f(x) = -xe^x$ is the same as that of $y = - x$ $y = -x$ .

Note that $y = - x$ $y = -x$ means that $x$ $x$ and $y$ $y$ are of opposite signs, except at $(0, 0)$ $(0, 0)$ .

So $f (x)$ $f(x)$ runs through Q2 and Q4, intersecting both axes at $(0, 0)$ $(0, 0)$ .

graph{-xe^x [-10, 10, -5, 5]}

Which quadrants and axes does f(x)=−xexf(x)=-xe^x pass through?