The graph of a polynomial has four turning points what is the least possible degree of this polynomial ? a.3 b.4 c.5 d.6

answer : 5

For example

The quadratic equation has 1 tuning point. The degree of quadratic polynomial is 2

Cubic polynomial can have 2 turning points. The degree of cubic polynomial is 3

From this we conclude that if a polynomial has 'n' turning points, then the least possible degree is n+1

the graph of a polynomial has 4  turning points, so the least possible degree is

4+1 = 5

5 is the least possible degree of this polynomial

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50