Step 4: Set the derivative equal to zero to find critical points: 3x^2 - 12x + 9 = 0.
Step 5: Factor the equation: (x - 3)(x - 1) = 0.
Step 6: Solve for x by setting each factor equal to zero: x - 3 = 0 gives x = 3, and x - 1 = 0 gives x = 1.
Step 7: The critical points are x = 1 and x = 3.
Finding Critical Points – This involves taking the derivative of a function and setting it to zero to find points where the function's slope is zero, indicating potential local maxima, minima, or points of inflection.
Derivative Calculation – Understanding how to correctly differentiate polynomial functions is crucial for finding critical points.
Factoring Quadratics – The ability to factor quadratic equations is necessary to solve for the roots of the derivative.
