Question

Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. f(x)=x^4-18x^2

Answer 1

find 1º derivative. Intervals where it's positive, function is increasing, where negative - decreasing

Answer 2

f´(x)=4x^3-36x

Answer 3

To find these intervals you must find the first derivative of f(x). Remember that the first derivative indicates the slope of the parent function. So if the first derivative is positive, the its increasing, if negative then decreasing.

Also note that the solutions of the first derivative are the max/min of the parent function.

So, \[f'(x)=4x^3-36x\]

The solutions are 0, 3 and -3

Thus we have four intervals where f(x) is either increasing or decreasing. These are \[(-\infty < x < -3) , (-3 < x < 0), (0 < x < 3), (3 < x < \infty) \]

Evaluate the first derivative at any arbitrary point in all four of the intervals to determine whether f(x) is increasing or decreasing.