We’ve been looking at physical applications of derivatives, but there are also economics applications. In this lesson, we’ll look at marginal cost, revenue, and profit. But before we jump into these marginal values, let’s look at cost, revenue, and profit in general.
Read MoreWhen we calculate average rate of change of a function over a given interval, we’re calculating the average number of units that the function moves up or down, per unit along the x-axis. Which means we always need to define a particular interval over which we’ll calculate the average rate of change of the function.
Read MoreThe optimization process is all about finding a function’s least and greatest values. If we use a calculator to sketch the graph of a function, we can usually spot the least and greatest values. The first part of the optimization investigation is about solving for critical points and then classifying them as representing local or global maxima or minima.
Read MoreGrowth and decay problems are another common application of derivatives. We actually don’t need to use derivatives in order to solve these problems, but derivatives are used to build the basic growth and decay formulas, which is why we study these applications in this part of calculus.
Read MoreRolle’s Theorem can prove all of the following: 1) The existence of a horizontal tangent line in the interval, 2) A point at which the derivative is 0 in the interval, 3) The existence of a critical point in the interval, and 4) A point at which the function changes direction in the interval, either from increasing to decreasing, or from decreasing to increasing.
Read MoreTo solve a related rates problem, complete the following steps: 1) Construct an equation containing all the relevant variables. 2) Differentiate the entire equation with respect to (time), before plugging in any of the values you know. 3) Plug in all the values you know, leaving only the one you’re solving for. 4) Solve for your unknown variable.
Read MoreVertical motion is any type of upwards or downwards motion that is constant. In a vertical motion problem, you may be asked about instantaneous velocity, and/or average velocity. To solve for instantaneous velocity we will need to take the derivative of our position function.
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