Derivative of the Inverse of a Function property in words: For any point (a, b) on an invertible function, the derivative of the inverse of this function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a.

Derivative of the Inverse of a Fucntion property in symbols:

Yes, volume is an invertible function, since it passes the horizontal line test.

The inverse function of volume:

Graph:

Proof: Equations

V(r)=(4/3)3.14r^3

y1=12.566(x-1)+4.1888

R(v)=(v/(4/3(3.14)))^(1/3)

y2=(1/12.566)(x-4.1888)+1

I took the derivative at the point (1, 4pi/3) and (4pi/3, 1).

Y1 and Y2 are the tangent lines.

As it shows, their slopes are reciprocals.

I chose to come to class that day. Firstly, I totally forgot we had the option to come to class or not to. Second, I think I learn better in classroom. So for my own benefit, I chose to come to the class.

## Sunday, January 24, 2010

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