6. The five graphs below have equal scales on the x and y axes. Which one could be the graph of y = 3x^{4} – 4x^{3} ?
A 
B 
C 
D 
E 

Solution: The answer is D
By the leading coefficient test we can disregard graph A. Since the leading coefficient is positive and the degree of y is even, then the graph of y rises to the left and right. Furthermore, factoring y yields,
The factor x^{3} results in a repeated zero of multiplicity 3 which accounts for three of the four real zeros of y and since the multiplicity is odd then it must cross the xaxis at x = 0. Which allows us to disregard graph B and E. The factor (3x – 4) results in a positive zero for y and hence we can disregard graph C. So, graph D, must be the graph of y.