To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
answer: was willing to help but you should’ve added a picture or added the choices there was to pick from because there isn’t much info.
Step 
In the right triangle ADB
<u>Find the length of the segment AB</u>
Applying the Pythagorean Theorem
we have
substitute the values
Step 
In the right triangle ADB
<u>Find the cosine of the angle BAD</u>
we know that
Step 
In the right triangle ABC
<u>Find the length of the segment AC</u>
we know that
solve for AC
Step 
<u>Find the length of the segment DC</u>
we know that
we have
substitute the values
Step 
<u>Find the length of the segment BC</u>
In the right triangle BDC
Applying the Pythagorean Theorem
we have
substitute the values
therefore
<u>the answer is</u>
