Question

How do you find the instantaneous rate of change of `y=5x+9` at x=2?

Answer 1

5

Explanation:

`y = 5x + 9` is a line in the form of `y = mx + b`

This means that the slope `m` at any point will the the same value, in this case, `5`. (Lines have constants slopes or rates of change.)

Using derivatives, we find that the `y' = 5` which confirms that the slope is `5` regardless of what the `x` value is. We only need to find the slope at a specific `x` value if the derivative has an `x` term in it.