How do you find the turning points of a cubic function?
The basic way to experience turning sharp-ends (maximums and povertys) of any part is the chief derivative trial. You to obtain?} the derivative of the part and set it similar to nothing (##f'(x) = 0##) or experience where it does not halt. Those values are determined nice quantity and are the singly places the part can modify order.
Once you keep your nice values you curb to see how the derivative modifys symbol at those sharp-ends. To do this you put in an x-value on twain sides of your nice sharp-end into the derivative. (For issue if your nice sharp-end is x = 2 then see what the symbol is of ##f'(1)## and of ##f'(3)##) If the derivative modifys from Positive (increasing) to Negative (decreasing) then you keep a culmination. If the derivative modifys from Negative to Positive you keep a poverty and if it has the identical symbol on twain sides the graph does not modify order there.
You can experience a amiable video about this at Khan Academy:Testing Nice Points for topical extrema