Does anyone know the answer to this??
Complete the definition:
A real function on an open Interval I is differentiable at x ∈ I if...
Is it to do with Rolle's Theorem, although that uses the property but doesnt actually define it?
Does anyone know the answer to this??
Complete the definition:
A real function on an open Interval I is differentiable at x ∈ I if...
Is it to do with Rolle's Theorem, although that uses the property but doesnt actually define it?
The answer to your question could be in many forms.
$\displaystyle \lim _{h \to 0} \frac{{f(x + h) - f(x)}}{h}=f'(x)$ if the limit exists.
But there are others.
Are you taking a course on Calculus or not? How could you possibly answer a question about "differentiable" if you have never been given a definition of "differentiable"?
Okay, here's a similar question- is the function $\displaystyle f(x)= e^{x^2}- x$ "codsquafalic". I am not, of course, going to define "codsquafalic"!
Hello there! Yes I am taking a course on Calculus and whilst I am aware of the process of differentiation from previous courses I have not been given a formal definition during this particular course.
The format Plato used earlier is along the lines of what I was hoping to achieve, I was just wondering how, using the same notation, would you define a critical point of a differentiable function?