Curve Sketching, Need help exam in 2 days

[thelazyman]

Hi, I have to sketch a graph with all of the following properties

- f is increasing when x < -2 and when -2<x<4

- f is decreasing when x > 4

- f'(-2) = 0, f'(4) = 0

- f is concave down when x < -2 and when 3<x<9

- f is concave up when -2<x<3 and when x >9

I realize that y"= 0 when x is -2, 3 and 9, and I think the formula for double prime is (x+2)(x-4) but I dont know how they find the x values in the equation and what equation they use:S.

Please help.

Thanks

 

[stapel]

I dont know how they find the x values in the equation and what equation they use.

They aren't asking for an equation, and the x-values are just demarkations of intervals. You need to mark of those intervals, and figure out what sort of curve to draw that might fit the conditions on that interval.

The answer will not be an equation, and there are infinitely-many correct answers (but many more incorrect ones).

Eliz.