Question

Three different purposes for determining the derivative.

Answer 1

See below

Step-by-step explanation:

A derivative is a slope function, so it allows you to find the slope anywhere along a function where it's continuous.

For example, the derivative of velocity is acceleration, which is applicable in real life.

You can also find a tangent line at a specific point by finding the slope of the function at that point and then using point-slope form
`y-y_1=m(x-x_1)` to get your tangent line.

Answer 2

A derivative is a slope function. If you want to find the slope anywhere along the function, you can.

Step-by-step explanation:

Given: What is the purpose of a derivative?

A derivative is a slope function: m=f'(x=value). If you want to find the slope anywhere along the function, you can.

If you want to find a tangent line at a specific point along the function you can, using the slope and the point: y−y1=m(x−x1)