Question

How do you find the instantaneous rate of change of the function `y= 5x - x^2` when x=-2?

Answer 1

`9`

Explanation:

The instantaneous rate of change is math for how fast something is going at a specific time. The shortened version of it is the derivative of a function - how fast the function is changing.

To find instantaneous rate of change, we simply take the derivative of our function, evaluate it at the point in question, and boom, we're done.

Let's begin. We have `y=5x-x^2`. Using the power rule, we find the derivative is
`y'=5-2x`

Next step is to find what this is when `x=-2`:
`y'=5-2(-2)`
`y'=5+4`
`y'=9`

Therefore, our derivative (instantaneous rate of change) at `x=-2` is `9`.