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Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2 What is _ x 0 f'(x) equal to?

Options

  1. A2
  2. B1
  3. C0
  4. DLimit does not exist

Correct answer

C. 0

Step-by-step solution

Given f(x) = cases x^3, & x^2 For x 0 , the relevant domain is x^2 In this interval, the function is f(x) = x^3 . Differentiating with respect to x , we get: f'(x) = 3x^2 Taking the limit as x 0 : _ x 0 f'(x) = _ x 0 3x^2 = 0 Answer: 0

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