Aprojectile is fired from a cliff 210 feet above the water at an inclination of 45 degree to the horizontal, with a muzzle velocity of 45 feet per second. the height h of the projectile above the water is given by h(x) = -32x^2/(45)^2 + x +210 where x is the horizontal distance of the projectile from the face of the cliff. use this information to answer the following.
at what horizontal distance from the face of the cliff is the height of the projectile a maximum? x = feet

31.64 feet

Step-by-step explanation:

The height is given by the equation:

where x is the horizontal distance of the projectile from the face of the cliff.

If the height is maximum, then its derivative must be h'(x)=0. Remembering that the derivative of is , we have:

And we want h'(x)=0, so:

This will give us the horizontal distance from the face of the cliff when the height of the projectile is at its maximum. We then do:

goog may have it for you

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8