Question

How is the derivative of a function related to the slop of the function?

Answer 1

Hi there!

The derivative of the function is the slope of the function at a specific x-value, or its instantaneous rate of change.

For example, take the equation y = x².

Using the power rule, we get:

y' = 2x

If we plug in any x-value into this equation, we can find the slope of the function at any point.

Ex:

x = 0; 2(0) = slope of 0

x = 2; 2(2) = slope of 4