SOLUTION: If f(x)= 2a|3x – 9| – ax, where a is some constant not equal to zero, find f ′(3). A.) 0 B.) not enough information C.) 1 D.) DNE Is the answer Does Not Exist

Algebra ->  Equations -> SOLUTION: If f(x)= 2a|3x – 9| – ax, where a is some constant not equal to zero, find f ′(3). A.) 0 B.) not enough information C.) 1 D.) DNE Is the answer Does Not Exist      Log On


   

Question 1090363: If f(x)= 2a|3x – 9| – ax, where a is some constant not equal to zero, find f ′(3).
A.) 0

B.) not enough information
C.) 1
D.) DNE
Is the answer Does Not Exist correct?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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|/0 - a ... note the term in red

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.