Algebra easy 10 points?

Question

The height of a rocket after t sec. is given by the function H(t) = 18t - 3t^2 

What is t at  maximum height.

A. 0 sec 

B. 2 sec 

C. 3 sec 

D. 18 sec 

The height of a rocket after t sec. is given by the function H(t) = 36t- 6t^2 

What is t at  maximum height.

A. 0 sec 

B. 3 sec 

C. 6 sec 

D. 36 sec

Answer 1

The rate of change in displacement is called velocity.

1) The function H(t) = 18t - 3t²

Apply derivative with respect of t.

dH/dt = 18 - 6t

At maximum height :  dH/dt = 0

0 = 18 - 6t

18 = 6t

t = 18/6

t = 3 sec

After 3 seconds the rocket reaches maximum height.

Option C is correct choice.

2) The function H(t) = 36t - 6t²

Apply derivative with respect of t.

dH/dt = 36 - 12t

dH/dt = v

At maximum height : dH/dt = 0

36 - 12t = 0

12t = 36

t = 36/12

t = 3 sec

After 3 seconds the rocket reaches maximum height.

Option B is correct answer.