Mathematics for Teaching Tag: derivative

## Tag: derivative

### Application of the Discriminant

The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. What is…

### 8 Different Ways to Think of the Derivative

In his paper The Transition to Formal Thinking in Mathematics, David Tall presents W.P. Thurston’s seven different ways to think of the derivative: Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function. Symbolic: the derivative of x^n is nx^n−1, the derivative of sin(x) is cos(x), the…

### Teaching maximum area problem with GeoGebra

Remember that classic maximum area problem? Here’s a version of it: Pam wishes to fence off a rectangular vegetable garden in her backyard. She has 18 meters of  fencing wire which she will use to fence three sides of the garden with the existing fence forming the fourth side. Calculate the maximum area she can…