Final answer:
To find the x-intercepts of the equation x^3 - 3x^2 + 4, you set the equation to zero and solve for x, which often requires numerical methods or graphing for cubic equations.
Step-by-step explanation:
To find the x-intercepts of the polynomial equation x^3 - 3x^2 + 4, you would set the equation equal to zero and solve for x. This corresponds to option (a). Finding the x-intercepts means finding the values of x where the function crosses the x-axis, which is where the function's value (y) is 0. However, this cubic equation doesn't factor easily, so you might need to use numerical methods or graphing to approximate the intercepts if factoring or simple algebraic methods (option b) don't work. Option (c), finding the derivative, is a technique used to find the slope of a function at a given point or to identify local maxima and minima, not the x-intercepts. Option (d), completing the square, is primarily used for solving quadratic equations, not cubic equations.