Author: Catherine

These two theorems allows us to prove statements about a function on an interval using derivatives. MVT Theorem (cr: Organic Chemistry Tutor) Rolle’s Theorem (cr: OCT and Mario’s Math Tutoring)

As the title suggests, this is looking for the most “optimal” solution using derivatives. Otherwise, the needed maximum or minimum. The steps to solve problems involving optimization are:1. Expressing the quantity needed to be optimized as a variable of only ONE unknown quantity 2. Finding the absolute maximum or minimum of the function by comparing…

Here we look at rates and the affect on/from position. We will be utilizing the implicit differentiation we learned before here. These are the main steps in solving these questions:1. Find the relationship between variables and create an equation based on this 2. Differentiate BOTH sides of the equation (must differentiate first before plugging any…

With curve sketching out of the way, we can look at other ways to apply derivatives. Those of you who have taken physics may recognize many terms from this lesson. Those who do not, here is a summary: Basic Physic Terminology (cr: Organic Chemistry Tutor) Now we apply what we have learnt so far in…

Looking at rational functions, we will be applying the same skills as the last lesson, however this time, we are considering how to find asymptotes using limits. We will also consider other discontinuities such as holes. Curve Sketching with Asymptotes (cr: Mr. S Math) Limits at Infinity & Horizontal Asymptotes (cr: Organic Chemistry Tutor) Sketch…

Taking EVERYTHING from 4.1-4.4 we will be sketching a curve! Curve Sketching (cr: Organic Chemistry Tutor) Sketching Derivatives (cr: Organic Chemistry Tutor) Given fx sketch the first and second derivative graph (cr: Brian McLogan)

This is looking at how the CURVE of the graph opens–concave up (positive parabola) or concave down (negative parabola). Definition: If a function’s graph is BELOW all of its tangent line, concave down. If a function’s graph is ABOVE all of its tangent line, concave up– hence why we use the 2nd derivative to determine…

The first derivative test is making a “sign diagram” via number line with the increasing/decreasing sketches to determine the nature of the extrema’s: relative if (-)->(+) or (+)->(-) no extrema if (-)->(-) or (+)->(+) Relative Extrema, Local Maximum and Minimum, First Derivative Test, Critical Points (cr: Organic Chemistry Tutor) First Derivative Test (cr: The Organic…

You may recall learning about maximum and minimum points on a parabola back in pre calc 11. Here we will looking at relative max/mins and absolute max/mins using derivatives. Note: endpoints of a function can be considered absolute max/mins, however not relative. These are otherwise known as “extrema”. Finding Local Maximum and Minimum Values of…

Welcome to application of derivatives! This is the first part in learning how to curve sketch! We will be looking at cases where f(x) is increasing (if f'(x) is +) or decreasing (if f'(x) is -) on a number line. Increasing and Decreasing Functions (cr: Organic Chemistry Tutor) Finding increasing interval given the derivative (cr: Khan…