```Question 48290
a.) Find the point of intersection for the graphs
{{{y=x^3+x-3}}}  and {{{y=2x +4}}}

Hit the button "y="
Enter by Y1 the x^3+x-3
Enter by Y2 the 2x+4
Hit the button "ZOOM"
Select  "6" STANDARD
Hit 2nd then CALC
Select "5" Intersect
The cursor will appear on the 1st curve.
Hit "ENTER"
The cursor moves to the line or 2nd curve.
Hit "ENTER"
Hit "ENTER" again to see the point of intersection.
It is x=2.0867... y= 8.1734...
That is the solution.
-------------------------------
b.) find the maximum value for the graph
{{{f(x)= -x^4 +x -4}}}
Hit 2nd "QUIT"
Hit "Y="
On the 1st line hit "CLEAR"
On the 2nd line hit "CLEAR"
On the Y1 line enter -x^4+x-4
Hit ZOOM
Select "6" STANDARD
HIt 2nd then CALC
Select "4" maximum
The cursor is on the curve to the left of the maximum point.
Hit ENTER
With the right arrow move the cursor to the right of the maximum point.
Hit Enter
Hit Enter again
The maxiumum is at x=0.62996... y=-3.5275....
-------------------------
c.) {{{f(x)=-x^4+x-4}}}.  On what intervals for "x" is "f" increasing?

You know the graph has its maximum at x=1.4893...
Looking at the graph you can see that it is rising to the left o
of that x-value.
So the "f" is increasing on the interval (-infinity,0.629950....
Cheers,
Stan H.```