The height, $h ( x )$ , of a punted rugby ball is given by $h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 9 } { 16 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point?
A)18 feet
B) 28 feet
C) 39 feet
D) 23 feet
E) 21 feet

Question

The height, $h ( x )$ , of a punted rugby ball is given by $h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 9 } { 16 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point? 
A)18 feet
B) 28 feet
C) 39 feet
D) 23 feet
E) 21 feet

Quizplus · Accepted Answer

The ball is at its highest point when the derivative of the height function is zero. The derivative of $h ( x )$ is $h'(x) = \frac { 1 } { 32 } x + \frac { 9 } { 16 }$. Setting $h'(x) = 0$ and solving for $x$ gives $x = 18$.

The Height h(x)h ( x )h(x) , of a Punted Rugby Ball Is Given By

The Height $h ( x )$ , of a Punted Rugby Ball Is Given By