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## Homework Statement

For f(x) = abs(x^3 - 9x), does f'(0) exist?

## The Attempt at a Solution

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The way I tried to solve this question was to find the right hand and left hand derivative at x = 0.

Right hand derivative

= (lim h--> 0+) f(h) - f(0) / h

= (lim h--> 0+) abs(h^3 - 9h) / h

= (lim h--> 0+) h^2 - 9

= (lim h--> 0+) h^2 - 9 = -9

Left hand derivative

= (lim h--> 0-) f(h) - f(0) / h

= (lim h--> 0-) abs(h^3 - 9h) / h

= (lim h--> 0-) -(h^2 - 9)

= (lim h--> 0-) -h^2 + 9 = 9

However, when I plug in the equation into the graphing calculator, the magnitude is correct, by the positive and negative signs are switched.