Question

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

Answer 1

Answer:

Option D - 64 feet.

Step-by-step explanation:

Given : 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.

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

Solution :

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

$f(x) = -16(x-2)^2 + 64$

Derivate w.r.t x

$f'(x) = -16\times 2(x-2)+0$      

$f'(x) = -32(x-2)$    

To find maxima put $f'(x)=0$

$0= -32(x-2)$      

$32x=64$        

$x=2$      

Now, we find the second derivative form maximum,

$f''(x) = -32$      

Therefore, The maximum point is at x=2

Substitute x=2 in the given function,

$f(2) = -16(2-2)^2 + 64$        

$f(2) = -16(0)+ 64$

$f(2) = 64$

Therefore, Option D is correct.    

The maximum height the ball reaches is 64 feet.                      

Answer 2

Answer:

DDDDDDD

Step-by-step explanation: