00:01
For this problem we are to find the following, the first one, the maximum number of turning points of a polynomial of degree 5, the minimum number of turning points, the maximum number of intercepts, and the minimum number of x intercepts.
00:17
Now to answer the first one, the maximum number of turning points, we have to note that the maximum number of turning points for a polynomial of degree n is always 1.
00:30
Less than its degree.
00:32
Therefore, the number of turning points here, the maximum number, is equal to 5 minus 1 or 4.
00:40
For the minimum number of turning points, it will be 0 because a polynomial function can have no turning point.
00:50
Remember that a turning point is like the point where the function changes its direction.
00:57
So when does a polynomial of degree 5 have no turning point? this is when we only have 1 0, and that's of multiplicity 5.
01:13
So if that's the case, say for example, the polynomial y equals x -rays to the fifth power.
01:22
This follows the graph of a cubic function and it looks like this, and you know, notice that there is no change in the direction of the graph here...