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Help pleasefind all points (x) where the function g(x)= |x+5| - |x-9| is not differentiable…

Help pleasefind all points (x) where the function g(x)= |x+5| - |x-9| is not differentiable-example-1
User Skeeter
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1 Answer

14 votes
14 votes

Given the function:


g(x)=|x+5|-|x-9|

Using the absolute value rules

So, the function will be written as follows:


f(x)=\begin{cases}-14;x\le-5 \\ 2x-4;-5So, we will check the points x = -5, x = 9 <p>Because the function has corners at these points</p><p></p><p>So, f'(x) will be:</p>[tex]f^(\prime)(x)=\begin{cases}0;x\le-5 \\ 2;59\end{cases}

As shown, the middle function is not equal to the function on the sides

So, the answer will be:

g(x) is not differentiable at x = -5, 9

User Yqbk
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