Given the following polynomial find the maximum possible number of turning points. f(x)=x6+x2+x7+x12

If you put in descending order you get:
f(x) = x^12 + x^7 + x^6 + x^2
The highest power (n) is 12 so the maximum number of turning points is (n - 1),  12 -1 = 11
You can have 11 turning points