Final answer:
The minimum value of the product xy for the given function y=4x^2 -3 is 0, which occurs when x is 0.
Step-by-step explanation:
To find the minimum value of the product xy, with y given by the equation y=4x^2 −3, we need to analyze the behavior of the function. First, notice that since y is a quadratic equation with a positive leading coefficient (4), the graph of y is a parabola opening upwards, meaning its vertex represents the minimum value of y. To find the vertex of the parabola, we remember that for a quadratic function in the form of ax^2 + bx + c, the x-coordinate of the vertex is given by -b/(2a). However, since there is no x term in the equation, the x-coordinate of the vertex is 0. Substituting x = 0 into the equation y=4x^2 −3, we find that the minimum value of y is -3.
Since x is zero at the minimum value of y, the product xy is also zero at the vertex of the parabola. Therefore, the minimum value of the product xy is 0.