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key term - Cubic function

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Definition

A cubic function is a polynomial function of degree three, typically expressed in the form $f(x) = ax^3 + bx^2 + cx + d$. The graph of a cubic function can have up to three real roots and two critical points.

5 Must Know Facts For Your Next Test

  1. The general form of a cubic function is $f(x) = ax^3 + bx^2 + cx + d$, where $a \neq 0$.
  2. Cubic functions can have one, two, or three real roots.
  3. The graph of a cubic function typically has an S-shaped curve with one inflection point.
  4. Critical points of a cubic function occur where the first derivative $f'(x)$ equals zero.
  5. The end behavior of a cubic function depends on the leading coefficient $a$: if $a > 0$, the graph rises to the right and falls to the left; if $a < 0$, it falls to the right and rises to the left.

Review Questions

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Cubic function - (Calculus I) - Vocab, Definition, Explanations | Fiveable | Fiveable