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.
50 dollars per month. It says "after x months" -50x is the variable thats changes.
Answer:
Step-by-step explanation:
3(2 + 4x) = -7 x 2 Distribute the 3
6 + 12x = -14 Subtract 6 from both sides of the equation
12x = -20 Divide both sides by 12
x = 
Divide the top and the bottom of the fraction by 4
x =
24) 9/19
27 is a bit tricky for me.. sorry ):
30) On the 7th it will be 1/120
33) C
