Striving to Succeed in Math Analysis: BQ #7: Unit V: Derivatives and the Area Problem

1. Explain in detail where the formula for the difference quotient comes from now that you know! Include all appropriate terminology (secant line, tangent line, h/delta x, etc).

The difference quotient is very significant in calculus and it is known as the derivative. The derivative is the slope of all tangent lines on the graph. The difference quotient is very helpful in finding all the possible slopes and curves that appear on any type of graph. A tangent line touches the graph once, whereas a secant line touches the graph twice. The y axis is notated as f(x), while the x axis is simply notated as x and x+h. Keep in mind that the letter h can also be written as delta x. The derivative, moreover, is written as f'(x) or "f prime of x". In this unit, you are not only doing the difference quotient, but you are also using it to determine the limit as h approaches 0. Once you find your derivative, you can use it to find specific values, slope, or the y=mx+b equation. Remember, the difference quotient is f(x+h) - f(x) divided by the letter h. This is similar to Y2-Y1/ X2-X1 (slope formula).

Example of a graph and plotted points using f(x)