f(x)=−4+x6−x3−3x−3x2−2x4−2x5 Based on the degree of the polynomial f(x) given below, what is the maximum...

Step 1
Turning Point: A turning point is a point of the graph where the graphchanges from increasing to decreasing or decreasing to increasing
Step 2
Note : A polynomial of degree n will have as most (n−1) turning points
${\displaystyle f\left(x\right)=-4+x^6-x^3-3x-3x^2-2x^4-2x^5}$
${\displaystyle =-2x^4-2x^5}$
degree (f(x))=6
${\displaystyle \therefore }$ f(x) can have 6-1 = 5 turning points i.e ,maximum number of turning points is 5