Question

How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-2x-8`?

Answer 1

See below

Explanation:

The first derivative should return the slope of the function, or to be more precise the equation that allows you to compute the slope of the function .

We have: `y(x)=x^2-2x-8`

In this case, the first derivative is:

`y'(x)=2x-2`

If we want a zero slope , we say that:

`y'(x)=2x-2 = 0 implies x color(red)(=) 1`

For a positive slope, so that `y(x)` is increasing as we move left - right along the x-axis, we say that:

`y'=2x-2 > 0 implies x > 1`

So the interval is: `x in (1, oo)`

And for a negative slope, so that `y(x)` is decreasing as we move left - right along the x axis, we say that:

`y'=2x-2 < 0 implies x < 1`

So the interval is: `x in (-oo, 1)`

We can plot it as well: