How to tell if a function is differentiable algebraically
- how to show a function is differentiable
- how to show a function is differentiable at a point
- how to show a function is differentiable on an interval
- how to prove a function is differentiable at 0
If a function is differentiable then it is continuous
How to know if a function is differentiable...
Continuity and Differentiability
Fully Explained w/ Examples!
Have you ever wondered what makes a function differentiable?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean?
It means that a function is differentiable everywhere its derivative is defined.
So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.
How To Determine Differentiability
By using limits and continuity!
The definition of differentiability is expressed as follows:
- f is differentiable on an open interval (a,b) if \(\lim _{h \rightarrow 0} \frac{f(c+h)-f(c)}{h}\) exists for every c in (a,b).
- f is differentiable, meaning \(f^{\prime}(c)\) exists, then f is continuous at c.
Hence, differentiability is when the slope of the tangent line equals the limit of the function at a given point.
This directly suggests that for a function to be differentiable, it must be continuous, and
- how to prove a function is differentiable real analysis
- how to show if a function is differentiable