2009-12-10, 08:31 AM
If you have a function f in an interval [a,b], then the minimum and maximum points are the points where the derivate either is 0 or undefined, or a or b.. For (a,b), this doesn't count (and thus doesn't count for infinity and such).
The function is increasing whenever the derivative is positive, and decreasing whenever the derivative is negative. That is, in an interval (a,b) given that a and b is either 0, undefined or (negative) infinity.
Concave up and down is the same as above, just for the double-derivative.
Points of inflection is where the double-derivative is 0 or undefined.
Noah
The function is increasing whenever the derivative is positive, and decreasing whenever the derivative is negative. That is, in an interval (a,b) given that a and b is either 0, undefined or (negative) infinity.
Concave up and down is the same as above, just for the double-derivative.
Points of inflection is where the double-derivative is 0 or undefined.
Noah