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## 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:

- A cubic differentiates to a quadratic (parabola)
- A the turning points have a gradient of zero and will move to the x axis on the derivative sketch
- A point with a positive gradient will be above the x axis in the sketch
- 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 , because this is where the turning points occur.

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

For the gradient is positive.

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

For 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

### Practice

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Categories: Differentiation

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