Question

webwork 2 - topics 4 - 5: (1 point) let ( f(x)=|x - 4|). evaluate the following limits. (lim_{x
ightarrow4^{-}}\frac{f(x)-f(4)}{x - 4}=) (lim_{x
ightarrow4^{+}}\frac{f(x)-f(4)}{x - 4}=) thus the function ( f(x)) is not differentiable at 4. note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have 6 attempts remaining.

Explanation:

Step1: Define the function for $x\to4^{-}$

When $x\to4^{-}$, $f(x)=-(x - 4)$. And $f(4)=|4 - 4| = 0$. Then $\frac{f(x)-f(4)}{x - 4}=\frac{-(x - 4)-0}{x - 4}=-1$.

Step2: Calculate the left - hand limit

$\lim_{x\to4^{-}}\frac{f(x)-f(4)}{x - 4}=\lim_{x\to4^{-}}\frac{-(x - 4)}{x - 4}=-1$.

Step3: Define the function for $x\to4^{+}$

When $x\to4^{+}$, $f(x)=x - 4$. And $f(4) = 0$. Then $\frac{f(x)-f(4)}{x - 4}=\frac{(x - 4)-0}{x - 4}=1$.

Step4: Calculate the right - hand limit

$\lim_{x\to4^{+}}\frac{f(x)-f(4)}{x - 4}=\lim_{x\to4^{+}}\frac{x - 4}{x - 4}=1$.

Answer:

-1
1