Describe a relationship modeled by the function f(x) = 4x3 − 72x2 + 320x
1 answer:
Answer:
- A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is:
The first step to factor it is to extract common factor 4x:
The second step is to factor the quadratic trinomial.
That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
- x is the desired (unknown) length
- 4x is 4 times the desired length
- x - 10 is 10 less than the desired length
- x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors:
- Volume = (4x)(x-10)(x-8)
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Answer:
(Missing part of the question is attached)
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
where the graph of its derivative is shown in the attachment
<h3>(a)</h3>If the function is differentiable at point
, the tangent line to the graph of
at 1 is given by the equation:
So we call the linear function:
We know the as it is given in the question, and
from the graph attached. Substitute in the equation of
.
At x=1, is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve
. Thus, The estimates are too large.
