Are there any functions which are unable to be differentiated?

As in, say I had a function #f(x)#, and the derivative #f'(x)#. Is there any function for #f(x)# where the equation for #f'(x)# cannot be worked out using any differentiation rules and instead have to be done graphically.

Answer 1

Perhaps this is the kind of thing you're wondering about.

#f(x)={(x^2sin(1/x), "if", x != 0) ,(0,"if",x = 0):}#.
#f# can be differentiated by the chain rule at all #x != 0#, but to show that #f'(0)=0# we use (need?) the definition of derivative.

Graphical techniques are only as accurate as our ability to graph and read the graph.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Yes, there are functions that are unable to be differentiated. These functions typically exhibit certain properties that make them non-differentiable at certain points or over certain intervals. Examples include functions with sharp corners, cusps, or vertical tangents, such as the absolute value function ( |x| ) at ( x = 0 ). Additionally, functions that have discontinuities or behave irregularly can also be non-differentiable.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7