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

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. Michele_Laino

alternatively, we note that the graph of your function is a parabola like this: |dw:1433063023555:dw| 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: $\Large {y_V} = - \frac{{{b^2} - 4ac}}{{4a}} = - \frac{{{{54}^2}}}{{4\left( { - 9} \right)}} = ...?$

5. anonymous

@AJ01 and @michele_laino Thanks a bunch, it means a lot :')