# Differentiable vs. Non-differentiable Functions

Differentiable and non-differentiable functions form essential components of mathematical analysis, each embodying distinct characteristics and behaviors. In calculus, differentiability signifies the smoothness of a function's graph, where the derivative exists at each point within its domain. Conversely, non-differentiable functions lack this property, exhibiting abrupt changes, corners, or vertical tangents, rendering them challenging to analyze using traditional differentiation methods. Understanding the disparities between these function types is fundamental in various fields, from optimization problems in engineering to modeling complex systems in physics and economics.

Questions

- How do you verify whether rolle's theorem can be applied to the function #f(x)=tanx# in [0,pi]?
- How do you find the partial derivative of the function #f(x,y)=intcos(-7t^2-6t-1)dt#?
- What does differentiable mean for a function?
- What is the difference between differentiability and continuity of a function?
- If a function is continuous along the interval [1,3], would it be differentiable at x=1 and x=3?
- What is the total differential of #z=x^2+2y^2-2xy+2x-4y-8#?
- Where is Rolle's Theorem true?
- Are there any functions which are unable to be differentiated?
- On what interval is the function #ln((4x^2)+9)# differentiable?
- What are some examples of non differentiable functions?
- If there was a hole in the line at (2,3) and there is another point at (2,1), then would the graph be differentiable at that point and why?
- How do you verify whether rolle's theorem can be applied to the function #f(x)=absx# in [-1,1]?
- If f(x) is continuous and differentiable and #f(x) = ax^4 + 5x#; #x<=2# and #bx^2 - 3x#; x> 2, then how do you find b?
- Let f(x) be a function satisfying |f(x)| ≤ x^2 for -1 ≤ x ≤ 1, how do you show that f is differentiable at x = 0 and find f’(0)?
- How do you verify whether rolle's theorem can be applied to the function #f(x)=1/x^2# in [-1,1]?
- We have #f:RR->RR;f(x)=x(x-2)#.Is #f# differentiable on #x=2#?
- Differentiate #sinx# #/# #5x# + #sec^2 x"# ?
- How do you determine the values of x at which #sqrt(x^2 + 9)# is differentiable?
- How do you verify whether rolle's theorem can be applied to the function #f(x)=x^3# in [1,3]?
- Verify that #f(x)# is differentiable at #x = 0#? #f(x) = x((e^(1//x) - 1)/(e^(1//x) + 1))#