Maxima and MinimaMedium
Question
Which of the following statements is true for the general cubic function f (x) = ax3 + bx2 + cx + d (a ≠ 0)
I. If the derivative f′(x) has two distinct real roots then cubic has one local maxima and one local minima.
II. If the derivative f′(x) has exactly one real root then the cubic has exactly one relative extremum.
III. If the derivative f′(x) has no real roots, then the cubic has no relative extrema
I. If the derivative f′(x) has two distinct real roots then cubic has one local maxima and one local minima.
II. If the derivative f′(x) has exactly one real root then the cubic has exactly one relative extremum.
III. If the derivative f′(x) has no real roots, then the cubic has no relative extrema
Options
A.only I & II
B.only II and III
C.only I and III
D.all I, II, III are correct
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