On what interval is the function f(x)=x^3-4x^2+5x concave upward?
1 answer:
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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
Check the picture below. You can pretty much count the units off the grid for its width and length.
