Solve the problem.
-The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function Find the relative maximum of the function.
A) (0, 6.9)
B) (175, 61.25)
C) (350, 129.4)
D) (175, 68.15)

Question

Solve the problem.
-The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function  Find the relative maximum of the function.
A) (0, 6.9) 
B) (175, 61.25) 
C) (350, 129.4) 
D) (175, 68.15)

Quizplus · Accepted Answer

To find the relative maximum, we need to take the first derivative of the function and set it equal to zero. Then, we solve for d to find the x-coordinate of the relative maximum, and plug that value back into the original function to find the corresponding y-coordinate (height).

Taking the first derivative of h(d), we get:
h'(d) = (1/50)e^(3d/700) - (3/700)e^(3d/700)

Setting h'(d) equal to zero, we can solve for d:
(1/50)e^(3d/700) - (3/700)e^(3d/700) = 0
e^(3d/700) = 3/50
d = (700/3)ln(3/50) = 175

So, the x-coordinate of the relative maximum is d = 175. To find the corresponding y-coordinate (height), we plug d into the original function:

h(175) = 61.25

Therefore, the relative maximum is at (175, 68.15) and the best choice is D.

Solve the Problem. -The Olympic Flame at the 1992 Summer Olympics Was Lit