Tina wants to put a ribbon around the mirror. She needs to find how much ribbion to buy. What measurement tool and unit would be
1 answer:
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To factor both numerator and denominator in this rational expression we are going to substitute 
with 
; so 
and 
. This way we can rewrite the expression as follows:
Now we have two much easier to factor expressions of the form
. For the numerator we need to find two numbers whose product is 
(30) and its sum 
(-11); those numbers are -5 and -6. 
and 
.
Similarly, for the denominator those numbers are -2 and -5.
and 
. Now we can factor both numerator and denominator:
Notice that we have
in both numerator and denominator, so we can cancel those out:
But remember than
, so lets replace that to get back to our original variable:
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is
Now we have two much easier to factor expressions of the form
Similarly, for the denominator those numbers are -2 and -5.
Notice that we have
But remember than
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is
Answer:
a) DNE
b) The function increases for every real value of x.
c) DNE
Step-by-step explanation:
Given a function f(x), the critical points are those in which , that is, the roots of the first derivative of f(x).
Those critical points let us find the intervals in which the function increases or decreases. If the first derivative in the interval is positive, the function increases in the interval. If it is negative, the function decreases.
If the function increases before a critical point and then, as it passes the critical point, it starts to decrease, we have that the critical point
(a) Find the critical numbers of f.
7 = 0 is false. This means that f has no critical points.
(b) Find the open intervals on which the function is increasing or decreasing.
Since there are no critical points, we know that either the function increases or decreases in the entire real interval.
We have a first order function in the following format:
In which .
So the function increases for every real value of x.
(c) Apply the First Derivative Test to identify the relative extremum.
From a), we find that there are no critical numbers. So DNE