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A cubic function is a polynomial of degree $3$; that is, it has the form $f(x) = ax^3 + bx^2 + cx + d$, where $a \not= 0$.(a) Show that a cubic function can have two, one, or no critical number(s). Give examples and sketches to illustrate the three possibilities.(b) How many local extreme values can a cubic function have?

(a) Proof in the video ; (b) A cubic polynomial can either have two local extrema or no local extrema

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Catherine R.

Missouri State University

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

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Video Transcript

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

Lectures

Join Bootcamp