Question

Find the open intervals on which the function is increasing or decreasing. g(x) = x^2 - 2x - 8

Answer 1

To find the intervals on which the function g(x) = x^2 - 2x - 8 is increasing or decreasing, we need to take the derivative of g(x) with respect to x and find where it is positive (increasing) or negative (decreasing).

g(x) = x^2 - 2x - 8

g'(x) = 2x - 2

Now we need to find where g'(x) > 0 (increasing) and where g'(x) < 0 (decreasing).

g'(x) > 0

2x - 2 > 0

2x > 2

x > 1

g'(x) < 0

2x - 2 < 0

2x < 2

x < 1

Therefore, g(x) is increasing on the interval (1, infinity) and decreasing on the interval (-infinity, 1).