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

1 Answer
Mar 30, 2017

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:

enter image source here