Oh i get it now
Also how would you do this question?
In order to locate the turning points of a cubic, you need to differentiate it's given equation.
- Now you basically need to solve for x
a) Since part a of the question wants you to justify that (5,-195) is a turning point of the given cubic, just sub in x = 5 into the equation.
Therefore (5, -195) is a minimum T.P. of the given cubic.
b) Well since only two x-values were discovered (and that there are two T.P.s), it means that the turning points displayed on the graphs are the only existing turning points of the function.
c) Using the same method utilised in part a of the question, you can determine the exact location of the maximum T.P (by subbing-in x= 3 into the equation).
Therefore, the exact location of the local maximum point is (-3, 61). Which seems correct, since the x coordinate has to be negative, and the y coordinate has to be positive (as seen on the graph).