Luke M.

asked • 11/13/22

Graph interpretation, piecewise

Using the graph of f(x) here:


https://www.desmos.com/calculator/g0va7vc9ml


May you explain at what points f(x) is discontinous and why? And where is f(x) NOT differentiable and why?

Egbert M.

Discontinuous means that a function has a "gap" at a certain independent variable (here x) in the values for the dependent variable (here y). Mathematically it means that the limits of the function(s) on either side of x (here x=3) are different (here 3 from the left side and + infinity from the right side). Non-differentiable means that the limits of the first derivatives on either side of a point x are not the same, or, graphically, there is no common tangent. Here, the tangent from the left is vertical (slope infinity, derivative 2/3*x^(-1/3)), while the slope from the right is -2 (derivative 2x-2).
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11/21/22

1 Expert Answer

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Abhimanyu C. answered • 02/14/23

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The function is discontinuous at x = 3, because there's a sharp break (you can't draw from left to right without lifting your pencil off the page. The function is also not differentiable there because differentiable functions are continuous.


The function is also not differentiable at x = 0, because there is a sharp kink in the graph there.



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