Which is the correct answer?
1 answer:
Answer:
D.
Step-by-step explanation:
The average rate of change of the function f is more than the average rate of change of x.
Here is why.
Look at the rates of change going from x = 0 to x = 3.
From x=0 to x=1, where x changes one unit, the value of f(x) only changes one-half unit, which is less than the change in x. But as you move to the right, see how the change in f(x) keeps getting larger and larger in magnitude? (Don't worry about the (-) sign.)
So, the <u>average</u> change in f will definitely be bigger than the average change in x, over the long run.
Now, look from x =0 and go back the other way, as x decreases 1 unit at at time. It is the same story.
If you would like to see this for yourself, look at the attached graphic.
Hope this helps.
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For a given girth, the largest area will be that of a square. Then for some length x, the volume will be
.. V = x((108 -x)/4)^2
.. = (1/16)*x*(108 -x)^2
The largest volume will be found where the derivative of this with respect to x is zero.
.. V' = (1/16)*((108 -x)^2 -2x(108 -x))
.. 0 = (108 -x)(108 -x -2x)
.. x = 108 or 108/3 = 36
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.. 36 inches in length and 72 inches in girth
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.. V = x((108 -x)/4)^2
.. = (1/16)*x*(108 -x)^2
The largest volume will be found where the derivative of this with respect to x is zero.
.. V' = (1/16)*((108 -x)^2 -2x(108 -x))
.. 0 = (108 -x)(108 -x -2x)
.. x = 108 or 108/3 = 36
The dimensions of the largest package that can be mailed are
.. 36 inches in length and 72 inches in girth
The volume of that package is 11,664 in^3.