# What are non differentiable points for a graph?

Since a function that is differentiable at

On the other hand, if the function is continuous but not differentiable at

1) the tangent line is vertical (and that does not have a slope)

2) the difference quotient

See this video on differentiability for details and pictures.

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Non-differentiable points on a graph occur where the function does not have a well-defined derivative. These points typically include corners, cusps, jumps, and vertical tangents. Additionally, non-differentiable points can occur at discontinuities, such as points where the function is not continuous or where there are vertical asymptotes. These points represent places where the slope of the function is undefined or discontinuous, making it impossible to calculate a derivative at those points.

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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.

- How do you find the slope of the tangent line to the graph of the given function # y=x^2#; at (2,3)?
- How do you find the equation of a line tangent to the function #y=x/(1-3x)# at (-1,-1/4)?
- Using the limit definition, how do you differentiate #f(x) = x^2 - 1598#?
- If #(2,6)# lies on the curve #f(x) = ax^2+bx # and #y=x+4# is a tangent to the curve at that point. Find #a# and #b#?
- How do you find the derivative of #f(x)=-5x# using the limit process?

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