# Open or Closed?

About this time of year you find someone, hopefully one of your students, asking, “If I’m finding where a function is increasing, is the interval open or closed?” Do you have an answer? This is a good time to teach some things about definitions and theorems. The place to start is to ask what it…

# Why Radians?

Calculus is always done in radian measure. Degree (a right angle is 90 degrees) and gradian measure (a right angle is 100 grads) have their uses. Outside of the calculus they may be easier to use than radians. However, they are somewhat arbitrary. Why 90 or 100 for a right angles? Why not 10 or…

# Difference Quotients II

The Symmetric Difference Quotient In the last post we defined the Forward Difference Quotient (FDQ) and the Backward Difference Quotient (BDQ). The average of the FDQ and the BDQ is called the Symmetric Difference Quotient (SDQ): You may be forgiven if you think this might be a better expression to use to find the derivative.…

# Difference Quotients I

Difference Quotients & Definition of the Derivative In the second posting on Local Linearity II, we saw that what we were doing, finding the slope to a nearby point, looked like this symbolically: This expression is called the Forward Difference Quotient (FDQ). It kind of assumes that h > 0. There is also the Backwards…