Consider the following function. f(x) = x4 - 24x3 + 162x2 + 7 Exercise (a) Make a sign diagram for the first derivative. Step 1 To make a sign diagram for the first derivative of f(x) = x4 - 24x + 162x2 + 7, we need the first derivative. Taking the derivative with the Power Rule, we have f'(x) = 4x3 - 72x2+ 324x 4x3 - 72x2 + 324.x Step 2 Now, we find the critical numbers of the function by setting the derivative equal to zero and solving by factoring 0 = 4x3 - 72x2 + 324x 4x/ Solving for x, we have the critical values. (Enter your answers as a comma-separated list.) X =