A manufacturer has determined that the price depends on the weekly demand based on the following function: p = f(q) = 10 – q² where p is the unit price and q is measured in units of a thousand (q = 1 means 1000 units). (a) Find the average rate of change in the unit price when the quantity demanded is between 1000 and 2000. (b) Find the average rate of change in the unit price when the quantity demanded is between 1000 and 1100. (c) Using limits, find the instantaneous rate of change in the unit price at the quantity 1000. No marks for using derivative rules (Section 4.3 and later).
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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