Author Topic: modulus derivative? (Read 646 times) Tweet Share

Yoda · « **on:** June 06, 2014, 10:45:05 pm »

Differentiate 3|x|-x^3 and express it as a hybrid function over a suitable domain.

b^3 · « **Reply #1 on:** June 06, 2014, 10:57:33 pm »

Since the modulus is only applied to $x$ and not the whole function, we do the domain split about $x=0$ .
$\begin{alignedat}{1}f\left(x\right) & =3|x|-x^{3} \\ f\left(x\right) & =\begin{cases} 3\left(-x\right)-x^{3} & \text{If }x<0 \\ 3x-x^{3} & \text{If }x\geq0 \end{cases} \\ f'\left(x\right) & =\begin{cases} -3-3x^{2} & \text{ If }x<0 \\ 3-3x^{2} & \text{If }x>0 \end{cases} \end{alignedat}$

Note that $x=0$ is not included, as we have a 'sharp' point at $x=0$ at the ends of where the domain is split. That is the gradient of the two curves is not equal at $x=0$ .
https://www.desmos.com/calculator/bb2zodfhyb

Champ101 · « **Reply #2 on:** June 06, 2014, 11:02:41 pm »

Quote from: Yoda on June 06, 2014, 10:45:05 pm

Differentiate 3|x|-x^3 and express it as a hybrid function over a suitable domain.

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Author Topic: modulus derivative? (Read 646 times) Tweet Share

Yoda

modulus derivative?

b^3

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Champ101

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