Question

If f(x) = 3a|4x - 4| - ax, where a is some constant not equal to zero, find f '(1)

Answer 1

The slope of an absolute function at the point where it evaluates to zero is undefined.
Here, when x=1, so |4x-4|=|4-4|=|0|, the slope is undefined.  This is where the vertex of the "V" on the graph of the absolute value function.

Answer 2

Answer:

Differential does not exist.

Step-by-step explanation:

given function,

f(x) = 3 a|4 x - 4| - ax

opening the function

f(x) = 3 a(4 x - 4) - ax              and        f(x) = - 3 a(4 x - 4) - ax    

f'(x) = 12 a - a                          and        f(x) = -12 a - a  

f'(x) = 11 a                                and        f(x) = -13 a    

f'(1⁺) = 11 a                                and        f(1⁻) = -13 a  

hence,

•                f'(1⁺)  ≠  f(1⁻)
• so, Differential does not exist.