Question

Why is \[x=0\] a critical point for \[f(x)=12x^{\frac{4}{3}}-6x^{\frac{1}{3}}\]?

Options

• \[f'(0)=1\].

• \[f(0)\] is not defined.

• \[f'(x)\] is not defined at \[x=0\].

• \[f(0)=18\].

Answer 1

The derivative contains \[x^{\frac{2}{3}}\] in its denominator. Therefore, \[f'(x)\] is not defined at \[x=0\], making it a critical point.