In a previous Math-FAQ, we looked at the different parts of a parabola. Based on this information, you know that to find the x intercepts of a parabola we need to solve a quadratic equation. When we solve a quadraticÂ equation to find the x intercepts of the graph, you might expect to always have solutions. But as the Math-FAQ below shows, this is not always the case.

]]>and in another as

These are basically the same formulas, but used in a different context. However, how you solve for the different quantities in either one is the same. The Math-FAQs below demonstrate how to solve forÂ

It can be difficult to distinguish between the bumps and dips on a graph, the relative (or local) extrema, and the very highest and lowest points on a graph, the absolute extrema.

The Math-FAQ belows show how to find each type of extrema using derivatives.

]]>Because of this, there are many FAQs available to help you work through these problems.

- Math-FAQ: How do you find the instantaneous rate of change?
- Math-FAQ: What is the difference between a secant line and a tangent line?
- Math-FAQ: How do you find the equation of a tangent line?
- Math-FAQ: How do you find a derivative at a point from the definition?
- Math-FAQ: How do you find the instantaneous rate from a table?

These examples should help you to solve problems from Section 11.2 and Section 11.3.

]]>This FAQ explores how to take a story problem and write it out as a system of linear equations.

]]>Excel comes in handy for creating tables of values for limits. This FAQ contains two PDFs that demonstrate the process of creating a table using a “fill” in Excel.

How Do I Make A Table Of Values In Excel?

This same process may be used to create tables in other types of spreadsheets such as Google Sheets.

]]>This FAQ shows how to take a tax table from the Arizona tax forms and convert it into a piecewise function.

In this FAQ we incorporate the idea that the amount you are taxed depends on the tax bracket you fit in.

This topics comes from Section 1 of Chapter 10 in Applied Calculus and is used in Section 5 of the same chapter.

]]>In Section 5.3, you are asked to find the rate in a sinking fund. Using the ordinary annuity formula results in an equation that is very difficult to solve. Instead, try graphing each side to the equation and locating the point of intersection.

]]>In many investment problems, you are given an amount of money and asked what will it accumulate to in a certain amount of time at some interest rate. Essentially, these problems are asking you to find the future value of the amount of money. Depending on how that money accumulates, you might use one of several different formulas.

The MathFAQ below looks at how you calculate present value in the context of different type of interest.

]]>Points of Inflection are locations on a graph where the concavity changes. In the case of the graph above, we can see that the graph is concave down to the left of the inflection point and concave down to the right of the infection point. We can use the second derivative to find such points as in the MathFAQ below.

What is the significance of this point? On both sides of the inflection point, the graph is increasing. This means that as the number of connections increased, so did the revenue from those connections. However, on the left side of the inflection point, the increases in revenue due to increasing connections is getting smaller and smaller. On the right side of the point of inflection, increasing the connections results in larger and larger increases in revenue.

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