We are standing on the top of a 1024 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h(t)=−16t2+192t+1024. What is the highest altitude that the object reaches?

The highest altitude of that object is 1,600 feet.

Step-by-step explanation:

Given that,

where h(t) is the height of the object after t seconds.

Differentiating with respect to t

h'(t)= -32t+192

Again differentiating with respect to t

h''(t)= -32

To find the maximum or minimum value, first we set h'(t)=0.Then we get a equation of t and solve it. Assume  t=a is the solution of the equation .

Now check h''(t) at t=a, if h''(a)<0 then the function h(t) has a maximum value at t=a

If h''(a)>0 then the function h(t) has a minimum value at t=a.

Now,

-32t+192=0

⇒32t=192

⇒t= 6

h''(6) = -32<0, So the object reaches at its highest altitude after 6  seconds.

Now plunging t=6 in the given function

h(6)= -16 (6)²+192×6 +1024

     =1600 feet

The highest altitude of that object is 1,600 feet.

25

step-by-step explanation:

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step-by-step explanation: