Gradient of Tangents

tangent of point

In a quadratic function or functions that have exponential powers, the gradient or slope changes all the time as curves determine them. During peaks or troughs, the gradients are zero, which will be later called stationary points. Inflexion points also have zero gradients, because the slope is treated as flat on that particular point.

Explore the gradient changes using the following Geogebra app.

 

In addition, the normal is a straight line perpendicular to the tangent at the same point of contact with the curve.

If lines with gradients m_{1} and m_{2} are perpendicular, then m_{1} m_{2}=-1

 

Example

Find the equation of the normal to the curve y=x^{3}+3x^{2}-2x-1 at the point (-1, 3).

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