To state: The increasing / decreasing test.
The Increasing/decreasing test:
1) If on an interval then is increasing on that interval.
2) If on an interval then is decreasing on that interval.
To explain: The meaning of concave upward curve on an interval.
If graph of a function f lies above all its tangents on interval I then f is known as concave upward over interval I.
In Figure 1, it is shown that for a concave upward curve the tangent lies below the graph of the curve while a concave downward curve the tangent lies above the graph of the curve.
To state: The concavity test.
The concavity test:
1) If for all x in I then graph of f is concave upward on interval I.
2) If for all x in I then graph of f is concave downward on interval I.
To define: The inflections points and explain the method of finding them.
“A point P on a curve is called inflection point if f is continuous at P and the curve changes from concave upward to concave downward or vice versa”.
An inflection point is at for any value of x where the concavity changes.
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