Elyssa bought a rectangular aquarium . The measurements , in feet (ft) , are shown below. How much water will it take to fill th
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Answer:
Step-by-step explanation:
To find the area of a rectangle you have to multiply the length by the width.
In your problem, the length and width are both equations, so you just have to multiply each part of the equation separately.
For example, if you were to put both equations with one over the other, you just have to multiply the aligned numbers.
The length is: x2 + 6x + 3
The width is: 3x2 + 4x - 2
and if you multiply the aligned numbers together, you get
3x2 + 24x - 6. Because:
x2 × 3x2 = 3x2,
6x × 4x = 24x,
and 3 × -2 = -6
Solution
For this case we can do the following:
And then if we multiply we got:
For convenience sake, I will let
First, we evaluate the function at the endpoints of the interval.
Then, we need to find the critical points.
We can start by taking the derivative using the power rule.
Setting this equal to 0,
Since , we can divide both sides by
.
So, the absolute minimum is and the absolute minima are