Respuesta :
The minimum value of the product is -8.
What is the minimum value?
The minimum value is the y value of the lowest point on the graph.
The function y = 2x-8 and we have to find the minimum value of the XY.
Plugging the value of y in the product;
[tex]\rm f(x)=x(2x-8)\\\\f(x)=2x^2-8x[/tex]
f(x) represents an upward parabola and we know that for an upward parabola, the minimum point is the vertex.
So in order to find the minimum value, we find the y coordinate of the vertex of the parabola.
The x-coordinate of the parabola is given by;
[tex]\rm = \dfrac{-b}{2a}\\\\=\dfrac{-8}{2\times 2}\\\\ =\dfrac{-8}{4}\\\\=-2[/tex]
The y -coordinate of the parabola is;
[tex]\rm f(x)=2x^2-8x\\\\f(2)=2(2)^2-8(2)\\\\f(2)=2\times 4-16\\\\ f(2)=8-16\\\\ f(2)=-8[/tex]
The vertex is (2,-8)
Hence, the minimum value of the product is -8.
Learn more about minimum value here;
https://brainly.com/question/3476532
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