A plane suddenly experiences turbulence while in flight. At this point the change in its altitude, in feet, is represented by the following function of time: $F ( x ) = \frac { 4 ( x - 8 ) ^ { 2 } - 6 } { 16 ( x - 8 ) ^ { 2 } - 8 ( x - 8 ) + 12 }$. Assuming that the turbulence first hits at time $x = 0$, what is the maximum relative drop the plane will experience due to turbulence? (Round the result to the nearest hundredth.)
A) 0.53 ft
B) 0.26 ft
C) 16.83 ft
D) 8.17 ft

Question

Quizplus · Accepted Answer

The given function simplifies to $F(x) = \frac{1}{4} - \frac{3}{4(4(x-8)^2-2(x-8)+3)}$. The maximum drop occurs when the denominator is at its minimum, which happens when $x = 8$, making the function value $F(8) = 0.25$. Since the question asks for the maximum relative drop, and considering the function represents the change in altitude, the maximum drop from the starting point is $0.25$ feet or $0.25$ rounded to the nearest hundredth, which is $0.25$ ft.

A Plane Suddenly Experiences Turbulence While in Flight F(x)=4(x−8)2−616(x−8)2−8(x−8)+12F ( x ) = \frac { 4 ( x - 8 ) ^ { 2 } - 6 } { 16 ( x - 8 ) ^ { 2 } - 8 ( x - 8 ) + 12 }F(x)=16(x−8)2−8(x−8)+124(x−8)2−6​

A Plane Suddenly Experiences Turbulence While in Flight $F ( x ) = \frac { 4 ( x - 8 ) ^ { 2 } - 6 } { 16 ( x - 8 ) ^ { 2 } - 8 ( x - 8 ) + 12 }$