Answer to Question #326695 in Calculus for Segun

Question

Suppose that we know f(x) is a polynomial with critical points x=-1, x=2 and x=6. If we also that the 2nd derivative is f''(x) = -3x² +14x -4. If possible, classify each of the critical points as relative minimums, relative maximums. If it is not possible to classify the critical points clearly explain why they cannot be classified.

Answer 1

x=-1

f"(-1)=-3-14-4=-21<0, then it is maximum

x=2

f"(2)=-12+28-4=12>0, then it is minimum

x=6

f"(6)=-216+84-4=-136<0, then it is maximum