189k views
2 votes
An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects maximum height if the equation of height (h) in terms of time (t) of the object is given by h(t) = -16t2 + 64t + 80?

2 Answers

3 votes
1) we calculate the first derivative:
h´(x)=-32t+64

2) we equalized to "0" the first derivative, and find out the value of "t".
-32t+64=0
-32t=-64
t=-64/-32
t=2

3) we calculate the second derivative:

h´´=-32<0 ⇒ then , we have a maximum at t=(2)

4) we calculate the height at t=2

h(2)=-16(2)²+64(2)+80=-32+128+80=176.

Answer: the maximum height is 176 m.
User Panofish
by
8.3k points
2 votes
ht + 16t2 - 64t - 80 = 0
ht - (((0 - 24t2) + 64t) + 80) = 0
3.1 Solve ht+16t2-64t-80 = 0
theres no solution found honey
User SowlM
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories