Derivative of Absolute Quadratic Function

Strategy:
1. Sketch parabola translated 1 unit down (x^2 - 1)
2. Absolute function returns positive values only.
Reflect negative part of the curve on x-axis
to get the Sketch of f(x)
3. Derivative at Cusp/Corner is not defined.
Therefore, define function as a piecewise function in 5 parts
dividing the domain at x-intercepts.
4. Sketch the derivative with table of values.

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[@blueinfluence521]

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[@mdazizulislam2425]

Very clear explanation. Thanks.

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[@reshampaudel9268]

Very clear explanation

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[@SuperSatyasrinivas]

Super explanation

[@utkarshnattamaisubramanian8437]

Amazing explanation sir.

[@dnyaneshwardalvi5828]

How can we identify coordinates of any local and absolute extreme points and inflection points of function y=|x^2-4|

[@adarsh3835]

At x=-1, value of derivative of f(x) is 3 but u have shown 2
Plz explain

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