Distance, y=-x^2+17x-66

Question

The shape of the hill can be described by the equation y=-x^2+17x-66 (x values between 6 and 11). Say that John has a rifle and is in his deer blind located at the point P_o=(2,0). Where on the hill is a deer safe from John's rifle? 

 

Answer 1

Taking the first derivative of this function and setting it equal to zero reveals the maximum point (top of the hill).

 

y = x²+17x-66 :: Original function

y'=17-2x :: First derivative

17-2x = 0 :: Set the first derivative to 0

x = 17/2 = 8.5 :: Solve for x

 

So long as the deer is at any point greater than 8.5, the hunter will not be able to shoot it.