Mathematics

Problem

The function

g(x)=|x|

is continuous at

x=0,

but

g'(0)

does not exist. Which of the following best explains the absence of the derivative at

x=0

? a) The tangent line to

g

x=0

is horizontal, giving a slope of

0

.},{ b)

\displaystyle \lim_{x\to 0}\frac{g(x)-g(0)}{x-0}

is infinite. c) The left-hand and right-hand limits of

\frac{g(x)-g(0)}{x-0}

are not equal as

x\to 0

.},{ d) The left-hand and right-hand limits of

g(x)

are not equal as

x\to 0

.}]},