Suppose that a device has been created that launches objects at ground level and that its operation is modeled by the function h(x) = -4ײ + 256x, with h being the height (in meters) and x being the distance (in meters) What is the maximum height that the object reaches?

$$ h\left(x\right)=-4x^2+256x $$ then h'(x) = -8x+256 For critical point; h'(x)=0 -8x+256=0 x=256/8=32 x=32 Now h''(x)=-8 which is less than 0, so the function give maximum value at x=32. So the maximum height = $$ -4\times32^2+256\times32=\:4096 $$