### Abstract

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Original language | English |
---|---|

Pages (from-to) | 144-148 |

Journal | International Journal of Mathematical Education in Science and Technology |

Volume | 47 |

Issue number | 1 |

Early online date | 28 May 2015 |

DOIs | |

Publication status | Published - 2016 |

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### Keywords

- Darboux's theorem
- derivative
- differentiable function
- mean-value theorem
- piecewise function

### Cite this

*International Journal of Mathematical Education in Science and Technology*,

*47*(1), 144-148. https://doi.org/10.1080/0020739X.2015.1049230

}

*International Journal of Mathematical Education in Science and Technology*, vol. 47, no. 1, pp. 144-148. https://doi.org/10.1080/0020739X.2015.1049230

**Calculating the derivative of piecewise functions.** / Johansson, B. Tomas.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Calculating the derivative of piecewise functions

AU - Johansson, B. Tomas

PY - 2016

Y1 - 2016

N2 - Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

AB - Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

KW - Darboux's theorem

KW - derivative

KW - differentiable function

KW - mean-value theorem

KW - piecewise function

UR - http://www.tandfonline.com/10.1080/0020739X.2015.1049230

UR - http://www.scopus.com/inward/record.url?scp=84930176375&partnerID=8YFLogxK

U2 - 10.1080/0020739X.2015.1049230

DO - 10.1080/0020739X.2015.1049230

M3 - Article

AN - SCOPUS:84930176375

VL - 47

SP - 144

EP - 148

IS - 1

ER -