Question

At where does y=54x -9x^2 have a maximum value? Using calc, pls...?

Answer 1

take the y' and the let the equation = 0 then solve it

Answer 2

y'=54-18x
y'=54-18x=0
solve for x
x=-54/-18=3

Answer 3

now use this value (3) in y=54x -9x^2
y=54(3)-9(3)^2
=162-81=81

(3,81)

Answer 4

alternatively, we note that the graph of your function is a parabola like this:

whose x-coordinate of vertex is:
\[\Large {x_V} = - \frac{b}{{2a}} = - \frac{{54}}{{2\left( { - 9} \right)}} = ...?\]
and the y-coordinate of the vertex, is:
\[\Large {y_V} = - \frac{{{b^2} - 4ac}}{{4a}} = - \frac{{{{54}^2}}}{{4\left( { - 9} \right)}} = ...?\]