Graph the function and identify all key characteristics f(x)=x^3-12x^2+45x-54

Mathematics

1 answer:

damaskus [11]3 years ago

8 0

Answer:

We kindly ask you to see the explanation and the image attached below for further details.

Step-by-step explanation:

From Function Theory we know that third order polynomials are continuous functions with one relative minimum and one relative maximum and whose domain and range comprehends the set of all real numbers. Since the leading coefficient of the polynomial is positive, then two increasing intervals and only one increasing interval exist.

Now we proceed to graph the function and label each relevant information when possible.

Domain

$Dom \{f(x)\} = \mathbb{R}$

Range

$Ran \{f(x)\} = \mathbb{R}$

Zeros

x = 3 and x = 6

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The perimeter of a rectangular construction site is 124 meters. The width is eight meters more than 5 times the length. Find the

tresset_1 [31]

Answer:

The perimeter of a rectangle is the sum of both lengths and both widths, which is equal to 54 meters. Let's call Length L and Width W.

The question is saying this: L = 3 meters + 3(W). We have 2 variables, which means we need at least 2 equations to solve. So far we have one, our second equation is from the perimeter.

2 lengths + 2 Widths = 54. Now, it's just a plug and chug.

2(3 + 3W) + 2W = 54.

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L = 3 + 3(6) = 21

To double check: 2(21) + 2(6) = 42 + 12 = 54

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