Concept explainers
Investigate the family of curves given by the equation f(x) = x4 + cx2 + x. Start by determining the transitional value of c at which the number of inflection points changes. Then graph several members of the family to see what shapes are possible. There is another transitional value of c at which the number of critical numbers changes. Try to discover it graphically. Then prove what you have discovered.
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Calculus: Early Transcendentals
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