Final answer:
The graph of the function y = 2x⁶ - 9x⁵ + 10x⁴ - x² has three points of inflection.
Step-by-step explanation:
The graph of the function y = 2x⁶ - 9x⁵ + 10x⁴ - x² can have points of inflection where the concavity of the graph changes. To find these points, we need to determine where the second derivative of the function equals zero.
The second derivative of the given function is y'' = 120x⁴ - 360x³ + 240x² - 2x. Setting y'' equal to zero and solving for x, we find that there are three possible x-values: x = 0, x = 1, and x = -1/60. Therefore, the graph of the function y = 2x⁶ - 9x⁵ + 10x⁴ - x² has three points of inflection.