Question 1090363
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Yes you are correct. Nice work. 


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This is what your steps should look like:


f(x) = 2a*|3x - 9| - a*x
f ' (x) = d/dx[ 2a*|3x - 9| - a*x ]
f ' (x) = d/dx[ 2a*|3x - 9| ] - d/dx[ a*x ]
f ' (x) = 2a*|3x-9|/(3x-9)*d/dx[ 3x - 9] - a
f ' (x) = 2a*|3x-9|/(3x-9)*3 - a
f ' (x) = 6a*|3x-9|/(3x-9) - a


Now plug in x = 3 into the derivative
f ' (x) = 6a*|3x-9|/(3x-9) - a
f ' (3) = 6a*|3*3-9|/(3*3-9) - a
f ' (3) = 6a*|0|/<font color=red size=4>0</font> - a ... note the term in <font color=red>red</font>


We stop here because we CANNOT divide by zero. So the answer is undefined leading to the result being DNE (does not exist).


Side Note: f(x) is a family of V shaped functions that have vertices of the form (3,k) where k is some real number. The value k will vary depending on what 'a' is.
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