Find the point at which the following function is a minimum: y = - 2x² + 3x + 6. A)x = 3 B)x = 1 C)x = 0 D)x = -3 E)None of the above

Question

Quizplus · Accepted Answer

To find the point at which the function is a minimum, we need to find the value of x that minimizes y. We can start by taking the derivative of y with respect to x and setting it equal to 0: y' = -4² + 3 -4² + 3 = 0 ² = 0.75 Substituting this value back into the original equation: y = 11eabb83_5a13_1074_b8db_b98d81f69d6b_TB2950_11 - 2(0.75) + 3x + 6 Simplifying: y = 11eabb83_5a13_1074_b8db_b98d81f69d6b_TB2950_11 + 1.5x + 6.75 To minimize y, we need to choose the value of x that makes the coefficient of x (1.5) equal to 0. This occurs when x = 3, so the answer is A.

Find the Point at Which the Following Function Is a Minimum