1.  By River, Gage, Travis, and Jack

2. Sections Chapter 6  6.1- Introduction to Differentiation (Gage)  6.2 - The Gradient Function (Gage)  6.3 - Calculating the Gradient of a Curve at a Given Point (River)  6.4 - The Tangent and the Normal to a curve (River)  6.5 - Rates of Change (Travis)  6.6 - Local Maximum and Minimum points (Travis)  6.7 - Using Differentiation in Modeling: Optimization (Jack)

3. 6.1 and 6.2 Introduction to Differentiation and Gradient Function  Finding the derivative:  F(x) : y=f(x) => dy/dx=f^1(x)=lim(f(x+h) – f(x))/h  If you have two functions f(x) and g(x) that are differentiable and have known derivatives then to find the derivative of the product of the two functions: You multiply the function by the derivative of the second function and add the second function times the derivative of the first.  The purpose of finding a derivative is to find the slope of a line when only one point is given to you. You can use this is multiple functions to determine the slope of a given line on a graph.

4. 6.3 Calculating the Gradient of a Curve at a Given Point  Step 1: Find the general gradient of the curve using dy/dx  Step 2: Substitute the x coordinate value of the given point into the expression found for dy/dx  Step 3: Graphing the gradient  Remember: You can use the gradient function to determine the exact value of the gradient at any specific point on the curve

5. 6.4 The Tangent and the Normal to a curve Tangent  Step1: Calculate b, the y- coordinate of P, using the equation of the curve  Step2: Find the gradient function dy/dx  Step3: Substitute a, the x- coordinate of P, into dy/dx to calculate, m is the value of the gradient at p  Step 4: Use the equation of a straight line (y-b) = m(x-a) Normal  Step 1: The normal is perpendicular to the tangent so its gradient, m, is using the formula m = -1/m where m is the gradient of the tangent

6. 6.5 Rates of Change To find the rate of change, you must find its slope Dependent variable _________________ Independent variable $20 = $5 5 1