Question

If y = 2x - 8 what is the minimum value of the product xy

Answer 1

Answer:

the minimum value of product  is -8

Step-by-step explanation:

We have been given the function y = 2x-8 and we have to find the minimum value of the xy.

Plugging the value of y in the product

$f(x)=x(2x-8)\\\\f(x)=2x^2-8x$

f(x) represents a upward parabola and we know that for a 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.

x-coordinate of the parabola is given by

$-\frac{b}{2a}\\\\=-\frac{-8}{2\cdot2}\\\\=2$

y -coordinate of the parabola is

$y=f(2)=2(2)^2-8(2)\\\\=8-16=-8$

Hence, the vertex is (2,-8)

Therefore, the minimum value of product  is -8

Answer 2

Hello : 
xy = x(2x-8)
let : f(x) = 2x²-8x
the derivate is : f'(x) = 4x-8
f'(x) = 0 ... x=2
sign f'(x) :   -∞   ــــــــــــــــــــــــــ2ـــــــــــــــــــــــ⟶ +∞
                         --------------  0  +++++++++
the minimum value of the product xy is the minimum value of f : 
f(2) = 2(2)²-8(2) =-8