Step 6: Solve for x by setting each factor to zero: x - 1 = 0 gives x = 1, and x - 3 = 0 gives x = 3.
Step 7: Now, find the y-values for the critical points by substituting x back into the original function f(x).
Step 8: Calculate f(1) = 1^3 - 6(1^2) + 9(1) = 1 - 6 + 9 = 4, so the first critical point is (1, 4).
Step 9: Calculate f(3) = 3^3 - 6(3^2) + 9(3) = 27 - 54 + 27 = 0, so the second critical point is (3, 0).
Step 10: The critical points are (1, 4) and (3, 0).
Finding Critical Points – This involves taking the derivative of a function, setting it to zero, and solving for x to find points where the function's slope is zero.
Evaluating Function at Critical Points – After finding the critical points, it is important to evaluate the original function at these points to determine their coordinates.
