Greatest value problems without derivatives
Set up a target function for a fenced rectangle, a rectangle in a triangle and a box, and read the greatest value from the vertex or from a table. State the domain of the variable.
- France: grade 7
- Germany: grade 10
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 6
Guide
In an extremum problem you first write the quantity to be made greatest as a function of one variable, the target function. For a rectangle with sides x and y and a fence condition you eliminate y first.
If the target function is quadratic, its greatest or least value is at the vertex of the parabola. For other functions read it from a table of values or a graph.
Always give the domain of the variable: lengths must be positive. The answer is a full sentence with the value and the unit.
The last mission (area of a triangle with a variable angle) belongs to the extended Realschule track (WPFG I).