Question

Hi tutor,What is the connection between the slope of a tangent of a function at a given point, and it’s derivative evaluated at that point? If possible, can you please use a diagram and derivation steps to help explain?

Answer 1

Given:

Derivative and sope of tangent

Required:

We want to define relation

Step-by-step explanation:

The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example

and the slope of that tangent is the derivative of function at point P

Now to find equation of a tangent line

1) Find the first derivative of f(x).

2) Plug x value of the indicated point into f '(x) to find the slope at x.

3) Plug x value into f(x) to find the y coordinate of the tangent point.

4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.