# Can a function be continuous and non-differentiable on a given domain??

Yes.

One of the most striking examples of this is the Weierstrass function, discovered by Karl Weierstrass which he defined in his original paper as:

This is a very spiky function that is continuous everywhere on the Real line, but differentiable nowhere.

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Yes, if it has a "bent" point. One example is

where the minus sign means approaching from left and plus sign means approaching from right.

Differentiable function practically means a function that steadily changes its slope (NOT at a constant rate). Therefore, a function that is non-differentiable at a given point practically means that it abruptly changes it's slope from the left of that point to the right.

Let's see 2 functions.

Graph

graph{x^2 [-10, 10, -5.21, 5.21]}

Graph (zoomed)

graph{x^2 [0.282, 3.7, 3.073, 4.783]}

Graph

graph{absx [-10, 10, -5.21, 5.21]}

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Yes, a function can be continuous and non-differentiable on a given domain. An example of such a function is the absolute value function ( f(x) = |x| ). This function is continuous everywhere, including at ( x = 0 ), but it is not differentiable at ( x = 0 ) because it has a sharp corner or "kink" at that point. This means that the derivative of the function does not exist at ( x = 0 ).

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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.

- What is the equation of the tangent line of #f(x) =sqrt(ln(cosx))# at # x = pi/4#?
- What is the equation of the line tangent to # f(x)=1/sqrt(x^2+3x+6) # at # x=-1 #?
- How do you use the limit definition to find the derivative of #y=-3x^2+x+4#?
- How to find an equation of the tangent line to the curve at the given point if #y=cosx-sinx# and #(pi,-1)#?
- What is the equation of the tangent line of #f(x)=cos^3x^2 # at #x=0#?

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