Perplex
Content
  • Exponents & Logarithms
  • Approximations & Error
  • Sequences & Series
  • Matrices
  • Complex Numbers
  • Financial Mathematics
  • Cartesian plane & lines
  • Function Theory
  • Modelling
  • Transformations & asymptotes
  • 2D & 3D Geometry
  • Voronoi Diagrams
  • Trig equations & identities
  • Vectors
  • Graph Theory
  • Probability
  • Descriptive Statistics
  • Bivariate Statistics
  • Distributions & Random Variables
  • Inference & Hypotheses
  • Differentiation
  • Integration
  • Differential Equations
Other
  • Review Videos
  • Blog
  • Landing Page
  • Sign Up
  • Login
  • Perplex

    Modelling (Lesson 4/10)

    Cubic Models

    1 / 2

    Discussion

    Amanda fixes magnets at positions x=−5cm and x=5cm. Then, she measures the force F applied to a third magnet at different positions. She plots her data on the graph below (negative positions and forces point toward Magnet 1, positive positions and forces point toward Magnet 2).

    Powered by Desmos

    Describe a curve that could be used to model force as a function of position.

    Solution:

    A good choice is a smooth, monotonically increasing S-shaped curve that goes through the points and has these visual features:

    • At the left (around x≈–3 cm) it sits down near F≈–8 units and is quite steep.

    • As you move toward the centre, the slope decreases, so by x≈–1 cm it’s already flattening off.

    • Between x≈–1 and x≈1 cm the curve is almost flat, passing through (0,0) with a gentle incline.

    • Beyond x≈1 cm the slope picks up again, becoming quite steep by x≈3 cm where F≈8 units.

    • The result is one continuous “S” shape, negative and getting steeper to the left, inflecting near x≈–1, nearly straight through the middle, then again near x≈1 to become steeper up to the right.

    Powered by Desmos