D(x)=-15x²+170.4x+3500.
There are two ways to solve this. First we can use calculus and differentiate:
dD/dx=-30x+170.4=0 at an extremum. We know that the equation is a parabola and the negative coefficient of x² tells us that it’s an inverted U shape, so the vertex is the maximum point. Therefore, x=170.4/30=5.68. The highest point is (5.68,D(5.68))=(5.68,3983.936).
Now, without calculus:
D(x)=3500-(15x²-170.4x)=
3500-15(x²-11.36x)=
3500-15(x²-11.36x+5.68²-5.68²)=
3500-15(x-5.68)²+15×5.68²=
3500+483.936-15(x-5.68)²=
3983.936-15(x-5.68)².
The minimum value of the squared term is zero, when x=5.68 so D=3983.936 as its maximum value, giving us the point (5.68,3983.936).