Solved Problems for Derivatives: MVT

Here we will look at some applications of the Mean value theorem and related statements.
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• Problem: Prove that for all real numbers x, y we have

  

• Problem: Prove that for all numbers t ≥ 0 we have

  

• Problem: Prove that the function

  f (x) = x⁴ + 6x² + 24x − 13

  has exactly two roots.