Differentiable vs. Non-differentiable Functions

Key Questions

• What does differentiable mean for a function?

  geometrically, the function #f# is differentiable at #a# if it has a non-vertical tangent at the corresponding point on the graph, that is, at #(a,f(a))#. That means that the limit
  #lim_{x\to a} (f(x)-f(a))/(x-a)# exists (i.e, is a finite number, which is the slope of this tangent line). When this limit exist, it is called derivative of #f# at #a# and denoted #f'(a)# or #(df)/dx (a)#. So a point where the function is not differentiable is a point where this limit does not exist, that is, is either infinite (case of a vertical tangent), where the function is discontinuous, or where there are two different one-sided limits (a cusp, like for #f(x)=|x|# at 0). See definition of the derivative and derivative as a function.

  Calculus V. · · Jul 25 2014

• What are non differentiable points for a function?
• What does differentiable mean for a function?
• What are non differentiable points for a graph?
• How do you find the non differentiable points for a function?
• How do you find the non differentiable points for a graph?
• What are differentiable points for a function?
• How do you find the differentiable points for a graph?
• What is the derivative of a unit vector?
• On what interval is the function #ln((4x^2)+9)# differentiable?
• How do you find the partial derivative of the function #f(x,y)=intcos(-7t^2-6t-1)dt#?
• How do you solve the differential equation #dy/dt = 2y - 10#?
• What are some examples of non differentiable functions?
• What is the total differential of #z=x^2+2y^2-2xy+2x-4y-8#?
• At where f(x)=|(x^2)-9| is differentiable?
• Can a function be continuous and non-differentiable on a given domain??
• Can a function be continuous and non-differentiable on a given domain?
• How to determine which of the following functions are one-to-one ?
• Question #491a2
• How do you determine the values of x at which #sqrt(x^2 + 9)# is differentiable?
• #inte^x[((sin^-1x)sqrt(1-x^2)+1)/sqrt(1-x^2)]dx# ?
• 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?
• 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?
• How do you determine the differentiability of f(x), where #f(x)=|x-1|+|x-2|+|x-3|#?
• 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)=tanx# in [0,pi]?
• How do you verify whether rolle's theorem can be applied to the function #f(x)=absx# in [-1,1]?
• How do you verify whether rolle's theorem can be applied to the function #f(x)=1/x^2# in [-1,1]?
• How do you verify whether rolle's theorem can be applied to the function #f(x)=x^3# in [1,3]?
• How do you prove from the definition of differentiability that the function #f(x)=(2x+1)/(x-2)# is differentiable?
• 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?
• Question #39963
• Given #(dr)/(dt)=(sect,tant,t^2)# calculate #r(t)# such that #r(0) = (0,0,3)# ?
• For what values of x is the function #f(x)=abs(x^2-9)# differentiable?
• Where is the function #h(x)=abs(x-1)+abs(x+2)# differentiable?
• Question #04706
• Given #f(x) = x^3-3x#, how can you construct an infinitely differentiable one-one function #g(x):RR->RR# with #g(x) = f(x)# in #(-oo, -2] uu [2, oo)#?
• Question #602c5
• Question #0b8db
• Question #831b1
• Question #400e8
• Differentiate #sinx# #/# #5x# + #sec^2 x"# ?
• Verify that #f(x)# is differentiable at #x = 0#? #f(x) = x((e^(1//x) - 1)/(e^(1//x) + 1))#
• Integrating factor question?