Choices

1. For any point (a.b) on an invertible function, the derivative of the inverse of the function evaluated at 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.

Below are the equations of the graphs exactly how I entered them into FooPlot

black(x)=(4/3)3.141x^3

red(x)=12.566(x-1)+4.1888

blue(x)=(x/(4/3(3.141)))^(1/3)

green(x)=(1/12.566)(x-4.1888)+1

6. I used the point (1, 4.188…)

f’(1) = 12.566…= slope of line tangent to f(1)

(f^-1)’(4.188…) = .0795= slope of line tangent to f^-1(4.188)

(12.5666)(.0795) = 1

7. I chose to come to class because I do not trust myself to learn a lesson of calculus online. I know that coming to class and being taught by Bru is reliable. When I learn from Bru directly, I know that I can expect to learn the new material thoroughly, having any questions, which I have a lot of, answered understandably. If I were to have taken the online path, I might not have understood the lesson due to different style or some other complication, and because I would be learning from a computer, any questions I might have had would go unanswered.