# Test you Knowledge: Applications of Derivatives

1. Find the maximum and minimum of on [0,3] First, we need to find the zeros of the derivative to determine where there are critical…

# Newton’s Method

Newton’s method provides a useful way to estimate the roots and solutions to equations. Suppose for instance we have a function , and we want…

# L’Hopital’s Rule

Throughout our work with limits and derivatives, we encountered a number of hard to solve limits. For example, consider . When determining the derivative of…

# Related Rates

Related rate problems are a type of problem where we have a rate, which is related to another, and we want to determine the rate…

# Mean Value Theorem and Rolle’s Theorem

The mean value theorem allows us to easily understand a number of useful facts about a function, such that it is continuous and differentiable. It’s…

# Maximum and Minimum Values

Now that we know how to take derivatives, we can start to learn about applications of them. One important application of derivatives is the ability…

This page will serve as a practice test for derivatives. We will go over some common derivative problems and see fully worked solutions for how…

# Derivatives of Exponential and Logarithmic Functions

The final derivative type that we need to investigate is the derivatives of exponential and logarithmic functions. First, let’s refresh on the definition of exponential…

# Implicit Differentiation

So far, we have seen functions that are easy to isolate for one variable. We typically have functions in the form of f(x) = [stuff]…

# The Chain Rule

With our current derivative rules, there are still some functions that we can’t take the derivative of. Take for example . We know how to…