Solve the Problem $y = x ^ { 3 } - 15 x ^ { 2 }$

question 274

Essay

Solve the problem.
-Find the inflection points (if any) on the graph of the function and the coordinates of the points on the graph whe function has a local maximum or local minimum value. Then graph the function in a region large enough to shor these points simultaneously. Add to your picture the graphs of the function's first and second derivatives.
$y = x ^ { 3 } - 15 x ^ { 2 }$

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Definitions:

Essential Component

A fundamental element or part necessary for the functioning or completeness of a system or whole.

Universe

The totality of all space, time, matter, and energy that exists, including galaxies, stars, planets, and all other forms of matter and energy.

Aerobic Respiration

A metabolic process in which cells use oxygen to break down glucose and other molecules, producing carbon dioxide, water, and energy in the form of ATP.

Selective Advantage

A genetic or behavioral characteristic that improves an organism's ability to survive and reproduce in its environment.