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

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) (Show Source): You can put this solution on YOUR website!

Yes you are correct. Nice work.

-------------------------------------------

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.

RELATED QUESTIONS
The given function f is one-to-one. {{{f(x)=(ax+b)/(cx+d)}}} a) Find the domain of (answered by stanbon)

Toni is solving this equation by completing the square. ax^2 + bx + c = 0 (where a is... (answered by nerdybill,rothauserc,Theo)

Which of the following is not a possible rational zero of f(x)= 2x^3-3x^2+2x-9? a. -1 (answered by stanbon)

Let f(x)=9+x+x ^2 and h not equal to 0. a. is f(8+1) = f(8)+f(1)? Yes or No (I... (answered by solver91311)

For how many values of x is the function not equal to 1? F(x)= (x-3) / (x-3) A)0 B)1... (answered by josgarithmetic)

A curve has gradient function f'(x) = ax+1 where a is constant. Find f(x) given that f(0) (answered by ikleyn)

Choose the statement that is true about the given quantities: A. The quantity in... (answered by jim_thompson5910)

Find the derivative of the following functions. Note that you need to use the Chain Rule (answered by ewatrrr)

True / False. If f is a linear function, then f(r+s)=f(r)+f(s). (A) True (answered by jim_thompson5910)

SOLUTION: If f(x)= 2a|3x � 9| � ax, where a is some constant not equal to zero, find f &#8242;(3). A.) 0 B.) not enough information C.) 1 D.) DNE Is the answer Does Not Exist

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