1) The Derivative of the Inverse of a Function says that for any point (a,b) on an invertible function, the derivative of the function's inverse evaluated at point b is equal to the reciprocal of the derivative of the function evaluated at point a.

2)

3) Volume is an invertible function

4)

5)

a)(4/3)*3.141592654x^3

b)12.566375(x-1)+4.1887902

c)(x/(4*3.141592654/3))^(1/3)

d).09403455(x-4.1887902)+1

6) My point (1, 4.1887902)

slope of tangent line at f(1)=12.566375

slope of tangent line at f'(2.3562)= 0.09403455

12.566375*0.09403455=1

7)I chose to come to class on Virtual Wednesday because I feel as though I learn better in a classroom environment. It provides structure and an atmosphere in which it is easier for me to focus. The resources of Bru and my classmates are of great help when I don't completely understand a concept. Learning from Bru and my classmates in a classroom as opposed to an online classroom is a much more reliable method of learning for me and is a more concrete way to learn the material. I have the opportunity to ask questions and am provided with a structured and complete lesson.

## Sunday, January 24, 2010

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Hey, using (a,b) in your definition really helped me get what you were saying. It also helped because your number two matched up exactly with what you said in number one.

ReplyDeleteI'm curious about your graph, though, none of the lines quite look like tangent lines. They should touch somewhere, right?

I'm sorry about that. The numbers I came out with for the slopes of the tangent lines were ongoing decimals. I couldn't quite fully enter them into the equation fully and so they turned out not so exact. Do you know of any way to enter them into the equation editor for the graphing program?

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