Question

Since there are no real roots for y² - 2y + 12, g'() exists for all real numbers. This means critical numbers occur where 0 = g'(y) = - y(12-y) This happens only when the numerator equals 0. Thus, the critical Thish (y² - 2y + 1202 numbers are as follows

Answer 1

The given equation y² - 2y + 12 does not have any real roots. The critical number for the equation is y = 1.

Step-by-step explanation:

The given equation is y² - 2y + 12. We need to determine if there are any real roots for this equation. To do this, we can calculate the discriminant using the formula b² - 4ac. For the given equation, a = 1, b = -2, and c = 12. Plugging these values into the formula yields (-2)² - 4(1)(12) = 4 - 48 = -44. Since the discriminant is negative, there are no real roots for the equation.

To find the critical numbers, we need to find where the derivative of the equation equals zero. The derivative of y² - 2y + 12 is 2y - 2. Setting this equal to zero, we get 2y - 2 = 0, which simplifies to y = 1. Therefore, the critical number is y = 1.