Partial Derivatives
Imagine you’re faced with the following function… …and asked to take the derivative with respect to y. How can you do that, considering that we’ve … Read More
Integrals with u-substitution
Consider taking the integral of the following function: Notice any issues? Any roadblocks we may run into? It’s easy enough to take the integral of … Read More
Definite Integrals
Recall the function f(x) that we worked with in Riemann Sums and Trapezoid Rule. When applying Riemann Sums (utilizing rectangles)… …and the Trapezoid Rule (utilizing … Read More
Integrals with Trapezoid Rule
In the Integrals with Riemann Sums article, we used rectangles to estimate integrals. Another common shape used to estimate integrals visually is trapezoids! This operates … Read More
Integrals with Riemann Sums
Imagine we’re traveling out west for a hiking trip, and throughout the entire road trip, we were traveling a constant 30mph, represented by f(x) below: … Read More
Sign charts (extrema & inflection)
We use sign charts to pinpoint important x-values on a given function. They are especially useful when we’re not given a visual of the function … Read More
Function Sketching
When prompted with a function sketching question like so… Question: Sketch a graph of the function y = f(x) where f(x) is concave down and … Read More
Integrals with initial condition
At the end of Integrals, we took the intergral of the marginal cost function, x/5… …resulting in the following equation for total cost. The +C … Read More