Question

Use your equations from Lesson 1 for the Brick candle and the Egyptian candle to create a graph of two polynomial functions so that you can compare volumes for different values of x. Compare the volumes.

My equations from lesson 1 were x^3-x^2 for the brick, and 7x^2 for the Egyptian.

Answer 1

9514 1404 393

Answer:

the cubic does not exceed the quadratic until x > 8

Explanation:

The attached graph plots the two expressions. The two are equal at x=8. Below that value the expression 7x^2 is greater. Above that value, the expression 7x^3 -x^2 is greater.

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Comment on the question

The directive to "compare the volumes" does not tell anything about the sort of comparison you are expecting. We note that the expression x^3-x^2 is zero or less up to the point where x=1, so we wonder exactly what it is supposed to be modeling. Any real volume will not be negative.

For small values of x, the quadratic is quite a bit larger. However, we know the cubic will grow larger than any quadratic for large values of x. So, the comparison you get will depend on the domain of interest—which is not specified.