Mathematics

Problem

For the function

f(x)=\sqrt[3]{x}

, which of the following best describes

f'(0)

? a)

f'(0)=0

because the tangent line is horizontal at the origin. b)

f'(0)=\infty

since

\displaystyle f'(x)=\dfrac{1}{3x^{2/3}}

and substituting

x=0

gives division by zero. c)

f'(0)

does not exist because the slope of the secant lines approaches

\pm\infty

x\to 0

. d)

f'(0)

does not exist because

f

is discontinuous at

x=0