Question

H(t) = –16t2 + 14t find the maximum height

Answer 1

The height is represented as y and the time is represented as x. 


To find the maximum height (since this is a parabola that faces downwards) we need to find the vertex.


Vertex (x) = $\frac{-(b)}{2a}$

b = 14
a = -16

Substitute
$\frac{-14}{2(-16)} = \frac{-14}{-32} = \frac{7}{8}$

Now plug 7/8 to t 
-16(7/8)^2 + 14(7/8)
-16(49/64) + 14(7/8)
-12.25 + 12.25
Answer: 0 ft

Answer 2

I suppouse the height is in  meters and the time is in  seconds. 

1) we calculate the first derivative:
H´(t)=-32t+14

2) we math the first derivative to "0"; and we find out the value of "X".
-32t+14=0
t=-14/-32
t=7/16

3) we calculate the second derivative:
H´´(t)=-32<0; then at t=7/16 we have a maximum.

4) we find out the maximun height.

H(7/16)=-16(7/16)²+14(7/16)
H(7/16)=-3.0625+6.125
H(7/16)=3.0625≈3.063

Answer: the maximun height was 3.063 m.


If the height is in ft; then the answer is 3.063 ft.