Final answer:
To graph the function and find the critical points, create a table of x and y values, plot these points on a coordinate plane, find where the derivative of the function equals zero or is undefined which gives the critical points.
Step-by-step explanation:
Based on the question, you need to graph the function y = -x^3 - 3x^2 + 3 and label the critical points. To begin with, you can create a table of values by substituting various x-values into the equation to obtain the corresponding y-values. In this case, the x-values could be -3, -2, -1, 0, 1, 2, and 3. Afterward, you would plot these points on a coordinate plane.
Next, to find the critical points, you have to find where the derivative of the function equals zero or undefined. The derivative of the function y = -x^3 - 3x^2 + 3 is dy/dx = -3x^2 - 6x. Setting this equal to zero gives x = 0 or x = -2. Substituting these values back into the original function gives two critical points (0,3) and (-2,11).
Lastly, you plot these critical points on the graph and connect all points with a smooth curve, and that's it. You've graphed the cubic function and identified and labeled its critical points.
Learn more about Graphing Functions