Home > Differentiation > Sketching derivative graphs (cubics)

## Sketching derivative graphs (cubics)

The important thing to remember here is that we are doing a sketch.  It does not have to be accurate, but id does have to conatian all the key points.

Hints:

1. A cubic differentiates to a quadratic (parabola)
2. A the turning points have a gradient of zero and will move to the x axis on the derivative sketch
3. A point with a positive gradient will be above the x axis in the sketch
4. A point with a pnegative gradient will be below the x axis in the sketch

Examples

Describe and sketch the derivative graph for the function below

The critical points are $x=0\mbox{ and }x=\frac{4}{3}$, because this is where the turning points occur.

These points will be on the x axis in the sketch.

For $x<0$ the gradient is positive.

These points will be above the x axis in the sketch.

For $0 the gradient is negative .

These points will be below the x axis in the sketch.

The graph is a cubic so the sketch will be a parabola