English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this article we discuss an important students' misconception aboutderivatives, that the expression of the derivative of the function contains theinformation as to whether the function is differentiable or not where theexpression is undefined. As a working example we consider a typical Calculusproblem of finding the horizontal tangent lines of a function. Following thestandard procedure, we derive the expression for the derivative using ProductRule. The search for the values of the independent variable, that make thederivative equal zero, leads to missing the unique solution of the problem. Weshow that in this case, even though the expression of the derivative isundefined, the function indeed possesses the derivative at the point. We alsoprovide the methodological treatment of such functions, which can beeffectively used in the classroom.

Teaching Differentiation: A Rare Case for the Problem of the Slope of the Tangent Line