Question: A cubic polynomial may have a local min and max, or it may have neither (Figure 27). Find conditions on the coefficients a and b

A cubic polynomial may have a local min and max, or it may have neither (Figure 27). Find conditions on the coefficients a and b of

1 1 f(x) x) = { x + @x+bx+c

that ensure f has neither a local min nor a local max.

+ -2 20 -20- (A) +X 4 -2 60 30 (B) N. 2 +X 4

1 f(x) x) = { x + @x+bx+c 1

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