6
votes
3answers
206 views

Is the complex derivative “speed”?

The first thing I was told about the real derivative is that it's "how fast the function is growing" at a given point. This interpretation wasn't addressed in my complex analysis classes. Can the ...
0
votes
1answer
36 views

Critical numbers of $x^{-5}\log x$

On a homework problem, I got the wrong answer and figured out what to put in for it to be marked correct (online homework), but I am unsure why it is right. The problem is to find the critical ...
0
votes
2answers
265 views

How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.

I don't know how to start the question. The title is self explanatory. How to approach and make a formal proof?
0
votes
1answer
63 views

First derivative

What would be the further steps for the case like this: I am finding the first derivative of a function: $f(x) = \ln(1+x^2)$ So the procedure would then be: $f'(x) = \frac{2x}{1+x^2}$. $f'(x) ...