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Which of the following statements is/are true?

Which of the following statements is/are true?

  1. If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].
  2. If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
  3. If f(x) is differentiable at x = c, then f(x) is continuous at x = c.




Given the relationship 2x2 + y3 =10, with y > 0 and dy/dt = 3 units/min., find the value of dx/dt at the instant x = 1 unit.

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