Ja'von kicks a soccer ball into the air. the function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. what is the maximum height the ball reaches?

2feet

16 feet

32 feet

64 feet

Option D - 64 feet.

Step-by-step explanation:

Given : Ja'Von kicks a soccer ball into the air. The function represents the height of the ball, in feet, as a function of time, x, in seconds.

To find: What is the maximum height the ball reaches?

Solution :

To find the maximum height of the ball we find the derivative,

Derivate w.r.t x

To find maxima put

Now, we find the second derivative form maximum,

Therefore, The maximum point is at x=2

Substitute x=2 in the given function,

Therefore, Option D is correct.    

The maximum height the ball reaches is 64 feet.                      

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