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

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प्रश्न

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

विकल्प

  • \[f'(0)=1\].

  • \[f(0)\] is not defined.

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

  • \[f(0)=18\].

MCQ
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उत्तर

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

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