Clip 1.  The nature of turning points using the Second Derivative. 

The second derivative is used to analyze the direction of Gradient Functions. 

The sign (or parity) of the second derivative, y”(x), evaluated at a point of interest is used to establish the nature of turning points in the categories of:

• • Minima (y”(x) > 0)
• • Maxima (y”(x) > 0)
• • Inflection (y”(x) = 0)

Clip 2.  Finding Tangents and Normals to a Curve using Calculus.

The use of calculus permits us to find the equations of normals and tangent to a single point on curves, which would have otherwise been very difficult!