Find the point at which the following function is a maximum: - 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 maximum, we need to find the value of x that makes the derivative equal to zero, and then check that it is indeed a maximum by checking the value of the second derivative at that point. The derivative of the function is -2² + 3, which is a linear function with a slope of -2² + 3. This means that the function is decreasing as long as x < (3/2²), and increasing as long as x > (3/2²). Therefore, the point at which the function is a maximum is at x = 1, which is the only possible maximum point according to the given choices.

Find the Point at Which the Following Function Is a Maximum