Respuesta :
Given the function:
[tex]f(x)=-7x^2+700x[/tex]It is a parabola of the form:
[tex]y=ax^2+bx+c[/tex]Then the parameters of the given parabola are:
a = -7
b = 700
c = 0
We have that if a<0 then the vertex is a maximum value. In this case, a = -7, therefore the function has a maximum.
To find the maximum, we find the coordinate of the vertex, which is given by:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x_{vertex}=-\frac{700}{2(-7)}=-\frac{700}{-14}=50[/tex]And we find y for the vertex:
[tex]\begin{gathered} y_{vertex}=-7(50)^2+700(50)=-7(2500)+35000=-17500+35000 \\ =17500 \end{gathered}[/tex]The vertex of the parabola is: (50, 17500) therefore the maximum is (50, 17500)
Answer:
maximum: (50, 17500)
minimum: none
