BQ #7: Unit V Concept- 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.) Your post must include text and some sort of media to support your writing.

-The difference quotient is used in higher level math, aka Calculus. In Calculus, the difference quotient is used when we talk about the concept: derivatives. We find the difference quotient by finding f(x+h), the simplifying f(x+h)-f(x) and at the end divide everything by h. When we divide by h we may need to take out a h from the numerator. The difference quotient to us was just this formula in the beginning but now we know that the difference quotient is also known as finding the slope of the tangent line to a graph. So the answer we got from the difference quotient formula is actually the slope of a tangent line aka the derivative. But before we can call it a tangent line we must change it from a secant line to tangent line. The picture below is an example of a secant line because it touches the graph twice.

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We change it from a secant line to a tangent line by plugging in zero whereever there is an h. So all the h's cancel out and makes it a tangent line. Once it is a tangent line we notice in the picture below that a tangent line only tocuhes the graph as we sae above that a secant line touches it twice. Now we have the derivative. 

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