This optional reflection is intended to be used after Exam 1, after you have also received your graded exam back. Here you can reflect on how the exam went and potentially help point to some factors that were successful or unsuccessful in your studies, so that you can better prepare for future exams.

Two young mathematicians discuss the novel idea of the ‘‘slope of a curve.’’

We compute the instantaneous growth rate by computing the limit of average growth rates.

Here we’ll practice finding the derivative using limits.

Two young mathematicians discuss derivatives as functions.

Here we study the derivative of a function, as a function, in its own right.

We see that if a function is differentiable at a point, then it must be continuous at that point.

Two young mathematicians think about ‘‘short cuts’’ for differentiation.

We derive the constant rule, power rule, and sum rule.

Two young mathematicians discuss derivatives of products and products of derivatives.

Here we compute derivatives of products and quotients of functions

We derive the derivative of sine.

We use the product and quotient rule to unleash the derivatives of the trigonometric functions.

Two young mathematicians look at graph of a function, its first derivative, and its second derivative.

Here we look at graphs of higher order derivatives.

Here we discuss how position, velocity, and acceleration relate to higher derivatives.

Two young mathematicians discuss the chain rule.

Here we compute derivatives of compositions of functions

Two young mathematicians discuss the standard form of a line.

In this section we differentiate equations without expressing them in terms of a single variable.

Here we’ll practice derivative rules.

Here we’ll practice finding lines tangent to curves.

Two young mathematicians race to math class.

Here we see a key theorem of calculus.

Two young mathematicians witness the perils of drinking too much coffee.

We use derivatives to help locate extrema.

We examine a fact about continuous functions.

Here we’ll practice on maxima and minima concepts.

This optional reflection is intended to be used before Exam 2. Here you can plan on how you intend to study for the exam. It will help you to think about how you can prepare for the exam and what resources you have at your disposal.