Question

1. why is it important to know where a function increases or decreases? give a real life example.

Explanation:

Understanding where a function increases or decreases helps in predicting trends, optimizing processes, and making informed decisions. In real - life, in a business context, the profit function of a company with respect to the number of units produced can be analyzed. If the profit function is increasing, producing more units within that range will lead to higher profits. If it is decreasing, producing more may lead to losses. For example, consider a small business that sells handmade candles. The profit function might initially increase as more candles are produced and sold due to economies of scale. But at a certain point, if too many candles are produced, the market may become saturated, and the price per candle may drop, causing the profit function to decrease.

Answer:

It helps in prediction, optimization, and decision - making. For example, a candle - selling business's profit function behavior with respect to production quantity.