Learning Resources

Investigation 4: Finding Maximum and Minimum Values

Test yourself (Answers)

Since the numbers differ by 20, if we let the smaller of the two be x the larger must be x + 20 (alternately we could let x be the larger, then x - 20 would be the smaller).  If we let the product be represented by y, the function rule is:

y = x ( x + 20 ) or y =  x² + 20x

Graph this function on the TI83 and use the [TRACE] to locate the minimum.

The minimum value for y (the product) is -100. The smaller number, x,  that gives this minimum product is -10 and the large number, x + 10, is 10. The two numbers that differ by 20 and give a minimum product are -10 and 10.