### The graph of a function f is shown. Which graph is an antiderivative of f?

This question explains the concept of antiderivative and how to draw its graph from the function graph. The antiderivative of a function is the indefinite integral of the function. If we take its derivative, it will give out the original function. The derivative and antiderivative or indefinite integral are inverse of each other. The derivative […]

### Where is the greatest integer function $f(x)= ⌊x⌋$ not differentiable? Find a formula for f’ and sketch its graph.

This question aims to find the points where the derivative of the greatest integer function or more commonly known as the floor function does not exist. The greatest integer function is the function that returns the nearest integer value to a given real number. It is also known as floor function and is represented by […]

### At a certain college, $6\%$ of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]