Calculate problems with resource constraints. An example of such a problem is where you only have 100 feet of fencing material to enclose an area. If you want to maximize the area enclosed by the fence, you should use calculus to find the best lengths for the enclosure. For this problem, you want to maximize the area, which equals length multiplied by width. However, you have the constraint that the perimeter must be 100 feet. You can write: maximize A = l*w subject to 2l + 2w = 100. Use algebra to solve for l, resulting in the answer l = 50 - w. Now plug this into the equation for A: A = (50 -- w)*w. To solve this, use calculus by taking the derivative and setting it equal to zero, giving: 50 - 2w = 0. So, w = 25. Now you know that you should make each wall 25 feet long to maximize the enclosed area.
Describe acceleration in terms of derivatives. Newtonian physics relies heavily on describing the motion of objects using calculus. You can explain acceleration in terms of derivatives by first writing: final velocity = initial velocity + (acceleration)*(time). You can then rearrange the terms to yield: acceleration = (final velocity -- initial velocity) / time. In other words, acceleration equals the change in velocity over the change in time -- precisely the definition of a derivative.
Analyze investment plans with calculus. With many choices for investing strategies, choosing the most suitable investment plan is a difficult task. Using calculus, you can calculate the interest versus the risk of certain investment plans. In addition, in high-level calculus, such as stochastic calculus, you use functions like Wiener processes and Markov chains to model the change in stock and option prices.