Question

Consider the function f(x)=3−4x² for −3≤x≤1.The absolute maximum value is and this occurs at x= _____________.

Answer 1

The absolute maximum value of the function f(x) = 3 - 4x² is 3 and it occurs at x = 0.

Step-by-step explanation:

The function f(x) = 3 - 4x² is a quadratic function with a downward facing parabola. To find the absolute maximum value, we need to determine the vertex of the parabola. The vertex of a quadratic function in the form f(x) = ax² + bx + c is given by the formula x = -b/2a. In this case, x = (-0)/(2(-4)) = 0. The maximum value occurs at x = 0 and can be found by substituting x = 0 into the function: f(0) = 3 - 4(0)² = 3. Therefore, the absolute maximum value is 3 and it occurs at x = 0.