Question

Find the intervals of increase and decrease given f(x)= x^3 - 6x^2

Answer 1

Find the derivative and your critical points. The intervals are the ones around those critical points. You can determine if the interval is increasing or decreasing by checking the derivative of a number in that interval -- if the derivative is positive, then it is increasing; if the derivative is negative, then it is negative.

Answer 2

critical points are 0 and 4

dont u use the original function to check?

Answer 3

i remember for something u use the original function, for something else u use the derivative function

Answer 4

The derivative will tell you the slope, which is basically how the graph is changing. The function itself will only tell us exact values of the function at a point. If we were to be testing with the function itself, we'd need at least two points per interval to determine that the graph has increased or decreased.