Hi I need some info on how to Sketch the square of functions.
Eg (x+6)(x+3)(x-4) Sketch the square and comment on the number of turning points.
Can someone find a website on this? I have searched google to no avail.
Thanks
Hi I need some info on how to Sketch the square of functions.
Eg (x+6)(x+3)(x-4) Sketch the square and comment on the number of turning points.
Can someone find a website on this? I have searched google to no avail.
Thanks
The function $\displaystyle f(x)=(x+6)^2(x+3)^2(x-4)^2$ is always greater than orOriginally Posted by classicstrings
equal to zero, it is increasing as $\displaystyle x \to \pm \infty$, and touches the $\displaystyle x$ axis when
$\displaystyle x=4,\ -3$ and $\displaystyle -6$.
Each of the zeros is a turning point, so it must have an additional turning points
between them making at least 5 turning points. Also it can have at most
five turning points (as $\displaystyle f'(x)$ is a quintic and so has five zeros
which are potential turning points), hence it has exactly 5 turning points.
This should be sufficient to allow you to sketch the curve.
RonL
Hello, classicstrings!
An interesting problem . . . I've never been asked to do this.
$\displaystyle f(x)$ is a cubic with x-intercepts: -6, -3, 4.$\displaystyle f(x)\,=\,(x+6)(x+3)(x-4)$
Sketch the square and comment on the number of turning points.
There are two turning points.$\displaystyle g(x) \,= \,(x=6)^2(x+3)^2(x-4)^2$ has the same x-intercepts but of order two.Code:| | * | ** | * -6 * * | * - - o - + - + - o - + - + - + - + - + - o - - - * -3* | * 4 * | * * *| * | ** |
. . The graph is tangent to the x-axis there.
Also the entire graph is above (or on) the x-axis.There are five turnning points.Code:| * | ** * ** |* * * * * *| * * * * * * | * * - - o*- + - + - o*- + - + - + - + - + -*o - - - -6 -3 | 4
Thanks for your help guys! The diagrams + explanations rock! CHeers!!!
EDIT: If you read what i posted before forget it!
EDIT: Soroban do you post on other maths help boards? I think I have seen you elsewhere.