Differentiable vs. Non-differentiable Functions - Page 3

  • Help with these 2 please?
  • If a function is continuous at a point, is it true that it is also differentiable at that point?
  • Why is the function not differentiable?
  • What is the correct option of the following question?
  • This statement is true or false?Please give reasons for your answer. Rolle's Theorem is applicable for the function f,defined by f(x)=1+x^(2/3) in the interval [-1,1] ?
  • If f‘(x) = g‘(x), then f(x) = g(x). Explain your answer if it is true. If false, provide a counterexample. True or False?
  • How do I use one sided derivatives to show that the function #f(x)=x^3 , x<=1# #f(x)=3x , x>1# is not differentiable at x=1?
  • Multiple Choice question: why is the answer B? I would think it's C.
  • What is the difference between the corollary and the second part of the Fundamental Theorem of Calculus?
  • Is there a difference between #d/(dx)[f(x)]# and #(df(x))/(dx)#?
  • What does it mean if a function is not differentiable at a point?
  • We have #f:RR->RR,f(x)={(x^2,,x inQQ),(0,,x in RR\\QQ):}#.How to verify if #f# is differentiable on #x=0# and #x=1#?
  • How are these calculus questions different?
  • How to find the points of of non-differentiability of a given function without graphs?
  • Example of a function that doesn't preserve monotonicity?