Use the derivative to locate all critical points. Use a graphing utility if desired. Round your answers to two decimal places.

Question

Use the derivative to locate all critical points. Use a graphing utility if desired. Round your answers to two decimal places.  ​

Quizplus · Accepted Answer

To locate critical points, we need to find the values of x where the derivative of the function is equal to 0 or undefined. Taking the derivative of the given function: f'(x) = 3x^2 - 12x + 9 Setting f'(x) = 0, 3x^2 - 12x + 9 = 0 x^2 - 4x + 3 = 0 (x-3)(x-1) = 0 x = 1 or x = 3 Checking the sign of f'(x) for x < 1, 1 < x < 3 and x > 3 to determine the nature of the critical points: For x < 1: f'(x) is negative For 1 < x < 3: f'(x) is positive For x > 3: f'(x) is negative Thus, x = 1 and x = 3 are critical points of the function. Option (C) is the correct answer as it lists both critical points.

Use the Derivative to Locate All Critical Points