## Wednesday, June 4, 2014

### BQ #7: Unit V: Derivatives and the Area Problem

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 helps us to find the slope of a tangent line at any point. But a tangent line only touches the graph once. While the secant line touches the graph twice. In order to find the slope of a secant line, we use the slope formula m = (y2-y1)/( x2-x1). So based on the first point on the graph below it is (x,f(x)) and the second point is (x+h, f(x+h)). So now we know what y2,y1,x2,x1 are. So we just plug this into the slope formula, which is m= (f(x+h))-(f(x))/((x+h)-(x)). So on the top nothing simplifies  but the bottom the 1s cancels out, which leaves us h for the denominator.

That will give us the difference quotient: Sometimes the delta x is refer to h.

http://www.infobarrel.com/Find_the_Derivative_of_a_function_by_using_the_difference_quotient_definition

Reference:
The text passage explains the derivation of the difference quotient, which is used to find the slope of a tangent line. It describes the relationship between the secant line and the tangent line, and how the slope formula for a secant line leads to the difference quotient.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Wednesday, June 4, 2014

### BQ #7: Unit V: Derivatives and the Area Problem

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 helps us to find the slope of a tangent line at any point. But a tangent line only touches the graph once. While the secant line touches the graph twice. In order to find the slope of a secant line, we use the slope formula m = (y2-y1)/( x2-x1). So based on the first point on the graph below it is (x,f(x)) and the second point is (x+h, f(x+h)). So now we know what y2,y1,x2,x1 are. So we just plug this into the slope formula, which is m= (f(x+h))-(f(x))/((x+h)-(x)). So on the top nothing simplifies  but the bottom the 1s cancels out, which leaves us h for the denominator.

That will give us the difference quotient: Sometimes the delta x is refer to h.

http://www.infobarrel.com/Find_the_Derivative_of_a_function_by_using_the_difference_quotient_definition

Reference:
user
The text passage explains the derivation of the difference quotient, which is used to find the slope of a tangent line. It describes the relationship between the secant line and the tangent line, and how the slope formula for a secant line leads to the difference quotient.

TYPE: NO_QUESTION