How to Use Differentiation to Calculate the Maximum Volume of a Box
One of the most practical uses of differentiation is finding the maximum or minimum value of a real-world function. In the following example, you calculate the maximum volume of a box that has no top and [more…]
How to Use Differentiation to Calculate the Maximum Area of a Corral
Finding the maximum or minimum value of a real-world function is one of the most practical uses of differentiation. For example, you might need to find the maximum area of a corral, given a certain length [more…]
Related Rates: the Expanding Balloon Problem
Say you’re filling up your swimming pool and you know how fast water is coming out of your hose, and you want to calculate how fast the water level in the pool is rising. You know one rate [more…]
Related Rates: the Trough of Swill Problem
Say you’re filling up your swimming pool and you know how fast water is coming out of your hose, and you want to calculate how fast the water level in the pool is rising. You know one rate [more…]
Related Rates: Two Cars at a Crossroads
Say you’re filling up your swimming pool and you know how fast water is coming out of your hose, and you want to calculate how fast the water level in the pool is rising. You know one rate [more…]
How to Determine Marginal Cost, Marginal Revenue, and Marginal Profit in Economics
Marginal cost, marginal revenue, and marginal profit all involve how much a function goes up (or down) as you go over 1 to the right — this is very similar to the way linear approximation works. [more…]
How to Do a Related Rate Problem Involving a Moving Baseball
You can use calculus to determine a rate that’s related to the speed of a moving object. For example, say a pitcher delivers a fastball, which the batter pops up — it goes straight up above home plate. [more…]
