Question

Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), seconds after Amir threw it, is modeled by h(x)=-(x+1)(x-7) How many seconds after being thrown will the ball reach its maximum height?

Answer 1

At 3 secs height will be maximum if height is modeled by h(x)=-(x+1)(x-7)

Step-by-step explanation:

h(x) = - (x + 1)(x - 7)

dh/dx = - ( (x + 1)(1)  + (1)(x - 7) )

=> dh/dx = - ( x + 1 + x - 7 )

=> dh/dx = -(2x  - 6)

=> dh/dx = 6 - 2x

6- 2x = 0

=> x = 3

d²h/dx²  = - 2

hence at x = 3  h will be maximum

After 3 secs ball will reach maximum height

Height = -(3 + 1)(3 - 7)

=> -(4)(-4)

= 16

After 3 secs ball will reach maximum height 16 m

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