<span>The function can only change from increasing to decreasing, and visa-versa at those points where the slope of the function is 0. And the slope of the function is determined by the first derivative of the function. So let's calculate the first derivative.
f(t) = (t^3 + 3t^2)^3
f'(t) = d/dt[ (t^3 + 3t^2)^3 ]
f'(t) = 3(t^3 + 3t^2)^2 * d/dt[ t^3 + 3t^2 ]
f'(t) = 3(d/dt[ t^3 ] + 3 * d/dt[ t^2 ])(t^3 + 3t^2)^2
f'(t) = 3(3t^2 + 3 * 2t)(t^3 + 3t^2)^2
f'(t) = 3(3t^2 + 6t)(t^3 + 3t^2)^2
Simplify
f'(t) = 3(3t^2 + 6t)(t^3 + 3t^2)^2
f'(t) = 3 * 3t(t + 2)(t^3 + 3t^2)^2
f'(t) = 9t(t + 2)(t^2(t + 3))^2
f'(t) = 9t(t + 2)t^4(t + 3)^2
f'(t) = 9t^5(t + 2)(t + 3)^2
And looking at the function, it becomes obvious that the roots (or inflection points) are at t = 0, t = -2, and t = -3.
Now the only places where f(t) can switch directions is at those 3 inflection points. And at exactly those inflection points the curve is neither increasing, nor decreasing.
If the slope of the function is positive, then its value is increasing, and if the slope is negative, then the function is decreasing. So all we need to do is calculate the value of the first derivative for any value between each inflection point plus one value smaller than the smallest inflection point and another value higher than the highest inflection point.
Range from [-infinity, -3)
f'(-4) = 18432
Since the value is positive, the function is increasing from [-infinity, -3)
Range from (-3, -2)
f'(-2.5) = 30.51758
Since the value is positive, the function is increasing from (-3, -2)
Range from (-2, 0)
f(-1) = -36
Since the value is negative, the function is decreasing from (-2, 0)
Range from (0, infinity)
f(1) = 64
Since the value is positive, the function is increasing from (0, +infinity)
To summarize:
increasing from [-infinity, -3)
increasing from (-3,-2)
decreasing from (-2,0)
increasing from (0,infinity]</span>
Let x and y be the no. of files of songs and pictures respectively
by 1st condition we get,
650x + 2200y = 18150
65 x+220y = 1815
13x + 44y = 363
by 2nd condition we get,
x+y = 16
now solve for x and y
and u ll get answer
Answer:
Option B
Step-by-step explanation:
Given that the required reserve ratio is 20 percent.
Since banks are conservative they choose not to loan all their excess reserves
i.e. only 20% of deposits is kept as reserve and 80% lent.
This 80% will again be deposited in a bank and 80% of 80 i.e.64% would be lent. Thus this will form a geometric progression infinitely as
deposits 
with common ratio 0.8<1
Hence infinite sum = 
So deposit multiplier is B) equal to 5
Answer:
78.5 ft²
Step-by-step explanation:
In this situation, the dog's 5 ft leash is the radius of the circle that he forms.
So, the radius is 5.
Use the area formula, A = 
r². Plug in 5 as r, and 3.14 as
A = r²
A = (3.14)(5²)
A = (3.14)(25)
A = 78.5
So, the area of the grass he can cover is 78.5 ft²
