# Need some help drawing a graph

• Jun 13th 2009, 11:25 AM
AMaccy
Need some help drawing a graph
I need to draw a graph with this information :

Graph a function on the interval [-2,5] with these characteristics:
relative max at x = -1
critical number at 0, but no extrema
absolute max at x = 2
absolute min at x = 5

how would i go about doing this and understanding this problem?
• Jun 13th 2009, 02:56 PM
apcalculus
Quote:

Originally Posted by AMaccy
I need to draw a graph with this information :
Graph a function on the interval [-2,5] with these characteristics:
relative max at x = -1
critical number at 0, but no extrema
absolute max at x = 2
absolute min at x = 5
how would i go about doing this and understanding this problem?

Set f(2) = 6 to be the absolute max.
Set f(5) = 0 to be the absolute min.

Start with f(-2) = 1 in concave down and increasing through f(-1) = 3. From x= -1 to x = 0 the graph can be concave down and decreasing. (Make sure at x=-1 you have a horizontal tangent.) At x = 0, the graph changes concavity from up down to up but keeps decreasing, so make sure at x=0 the graph has a vertical tangent (critical number, since the first derivative is undefined).

If you want the function to be continuous you may need to allow for another critical number. Otherwise, draw a vertical tangent somewhere between x=0 and x = 2, and ensure that x=2 is the 'highest' point. and x=5 is the 'lowest' point. I hope this helps.