Relative Minimum:
Definition: A value is said to be minimum, when its value is less than other values of the function.
A value of a function at a point x0 which is equal to or less than the values of the function at all points in some neighborhood of x0.
A minimum value can also be called a turning point of a function, because the curve changes its direction at that point. Do all curves have a minimum? Not necessary.
Example is a linear function. Consider a straight line graph. No minimum for this. Example of a curve having minimum is a parabola.All parabolas have either minimum or maximum value.
Minimum can also be interpreted as follows:
a. The least possible quantity or degree.
b. The lowest degree or amount reached or recorded; the lower limit of variation.
c. The smallest in a finite set of numbers
d. A value of a function that is less than any other value of the function over a specific interval.
a.Also called relative minimum, local minimum. the value of a function at a certain point in its domain, which is less than or equal to the values at all other points in the immediate vicinity of the point. Compare absolute minimum.
These are examples of curves with no minimum or turning points.
Definition: A value is said to be minimum, when its value is less than other values of the function.
A value of a function at a point x0 which is equal to or less than the values of the function at all points in some neighborhood of x0.
A minimum value can also be called a turning point of a function, because the curve changes its direction at that point. Do all curves have a minimum? Not necessary.
Example is a linear function. Consider a straight line graph. No minimum for this. Example of a curve having minimum is a parabola.All parabolas have either minimum or maximum value.
Minimum can also be interpreted as follows:
a. The least possible quantity or degree.
b. The lowest degree or amount reached or recorded; the lower limit of variation.
c. The smallest in a finite set of numbers
d. A value of a function that is less than any other value of the function over a specific interval.
a.Also called relative minimum, local minimum. the value of a function at a certain point in its domain, which is less than or equal to the values at all other points in the immediate vicinity of the point. Compare absolute minimum.
b.the point in the domain at which a minimum occurs.
How to find minimum:
1. By drawing the curve and seeing where it is the least value.
2.
Scientific method is application of Calculus. Finding derivatives and
equating first derivative to 0. We get a turning point. It can be
maximum or minimum. If second derivative is positive, then that point is minimum.
Uses of Relative Minimum in real Life:
1. In Economics, value for minimum price of a commodity
2. In costing, minimum production to break even.
3. In examinations, minimum marks for passing
4. In Business, minimum price at which seller is ready to sell. If it goes below this level, he will opt for holding instead
of selling.
5. In elections, minimum number of contestants to conduct an election
6. In medicine, minimum weight for a new born to survive.
7. In weather forecasting, minimum temperature
8. In recruitment, minimum salary a person expects to join
9. In electricity, telephone, minimum fixed charges a consumer has to pay irrespective of usage
Parabolic Curves
These are curves where minimum value is there and can be easily found out from the curve;
These are examples of curves with no minimum or turning points.
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