Write
-4x+2" align="absmiddle" class="latex-formula"> in the form of 
and solve
1 answer:
Because the coefficient of x^2 is -1, we know that a will be -1. Knowing that the coefficient of x is -4, we can calculate that p=2. Thus, we have -1(x+2)^2+q is our equation. This is equal to -x^2-4x-4+q. As the constant term must be 2, we can then see that q is 6.
As such, we have -1(x+2)^2+6=0 as our factorization.
To solve this equation, we can use the quadratic formula. Plugging in values, we have:
which is equal to: (when the fraction is simplified)
As such, we have -1(x+2)^2+6=0 as our factorization.
To solve this equation, we can use the quadratic formula. Plugging in values, we have:
which is equal to: (when the fraction is simplified)
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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