1. For every invertible function, the derivative of its inverse function is the reciprocal of the derivative of the initial function.

2.

3. Yes it is an invertible function, because:

(in black on the graph, and its derivative at x=1is in blue)

(in red on the graph and its derivative at x=1 is in green)

6. The slope of the tangent line at x=1 on V(r) is 12.56 and the slope of the tangent line at x=1 on r(V) is 1/12.56, and these two numbers are reciprocals.

Then, since the derivative at a point is the same as the slope of the tangent line at that point, the derivatives of the two functions V(r) and r(V) are reciprocals.

7. On "Virtual Wednesday" I chose not to go in the face-to-face class because I wanted to try something new. I had the intention of going in class probably for the last half of class, just in case I found difficulties learning on my own. I used http://www.analyzemath.com/calculus/Differentiation/derivative_inverse.html .

This website was helpful and easy to follow in the beginning, but as I kept doing exercises, I figured out that this rule about the inverse functions doesn't apply to trig functions, and then I stopped, and used the in-class exploration.

Check your derivative statement for number one, its different than what other people are saying, and from what you say in number two.

ReplyDeleteCool graph.

Thanks kwad, for the corrections.

ReplyDelete