Calxsolver
Subject:  Graphing

Analyse f(x) = x³ − 3x

Find the zeros, extrema and monotonicity of a cubic function.

Answer 3 zeros, 2 extremuma

Solution

  1. Function f(x) = x^3 - 3*x
  2. Domain analysed [-3, 3]
  3. Zeros -1.73205, 0, 1.73205
  4. y-intercept (0, 0)
  5. Local extrema max at (-1, 2); min at (1, -2)
  6. Monotonicity (-3, -1) ↑, (-1, 1) ↓, (1, 3) ↑
  7. Vertical asymptote candidates None detected.
  8. End behavior f(-3) = -18, f(3) = 18
  9. Range on interval f ∈ [-18, 18]

Try a similar problem yourself

Use the Function Feature Analyser to solve a similar problem with your own values.

Open the solver

More Graphing problems

Graph y = x² − 4 Plot a parabola and read off its zeros, vertex and y-intercept. Where does y = x² meet y = 2x + 3? Plot two functions and find their intersection points.