The following statements concerning the location of an extreme value of a twice-differentiable function, f, are all true. Which statement also includes the correct justification? (A) The function has a maximum at x=5 because f' (5) = 0. (B) The function has a maximum at x=5 because f' (x) <0 for x0 for x>5. (C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal. (D) The function has a minimum at x=3 because f' (x) <0 for x0 for x>3. (E) The function has a minimum at x=3 because f" (3) <0.

Question

Mathematics

Danica Oliver

24 April, 01:39

The following statements concerning the location of an extreme value of a twice-differentiable function, f, are all true. Which statement also includes the correct justification? (A) The function has a maximum at x=5 because f' (5) = 0. (B) The function has a maximum at x=5 because f' (x) <0 for x0 for x>5. (C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal. (D) The function has a minimum at x=3 because f' (x) <0 for x0 for x>3. (E) The function has a minimum at x=3 because f" (3) <0.

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Braedon · Answer 1

After thorough researching, the statement that also includes the correct justification is the statement in letter C that states that the function has a minimum at x=3 because the tangent line at x=3 is horizontal. The correct answer to the following given statement above is letter C.