PDF-In this section we will use the derivative to tell us if the graph is

constant Indicate all extrema max and min 242xxxfxF02DxF03Dincreasing as we move from left to right if the graph is going uphill then it is increasing Likewise if we move from left to. We have that AA 1 that is that the product of AA is the sum of the outer products of the columns of To see this consider that AA ij 1 pi pj because the ij element is the th row of which is the vector a a ni dotted with the th column of which is Notation dx dx y 00 f 00 Thus dx dx dy dx Example Find the second derivatives of the following functions a 2 x y 00 2 b y 00 c 5 4 5 y 00 The 64257rst derivative gives information about whether a funct ion increases or decreases In fact A d Relating f, f’, and f” . Problem A. Problem B. Conceptual Problems. Inability to see derivative as a function, only a value. Derivative is object but not as an operation. Derivative vs. Differentiation vs. “Finding the derivative”. Points of Inflection. Section 4.3a. Writing: True . or . False – A . critical point . of. a function always signifies . an . extreme. value . of the . function. Explain.. FALSE!!! – Counterexample???. Objective: Understand the relationship between differentiability and continuity. Miss . Battaglia. BC Calculus. Differentiability & Continuity. Alternative limit form of the derivative:. provided this limit exists. Note the limit in this alternative form requires that the one-sided limits. Example. For. . find the derivative of . f. and state the domain of . f’. . The derivative can be regarded as a new function. Example. Given the graph of the function, . f. Quotient Rule. Objective:. Students will be able to use the product and quotient rule to take the derivative of differentiable equations . Review: Definition of Derivative. The derivative of . f. at . Section 3.2a. A function will not have a derivative at a point . P . (. a. , . f. (. a. )) where. the slopes of the secant lines,. How . f. (. a. ) Might Fail to Exist. f. ail to approach a limit as . Chapter 3.1. Definition of the Derivative. In the previous chapter, we defined the slope of the tangent line to a curve . at a point . as. When this limit exists, it is called the . derivative of . Power, Sum, and Difference Rules, Higher-Order Derivatives. The “Do Now”. Find the derivative of. Does this make sense graphically???. The “Do Now”. Find the derivative of. Let’s see some patterns so we can generalize. nd. Derivative Test. Objectives:. To find Higher Order Derivatives. To use the second derivative to test for concavity. To use the 2. nd. Derivative Test to find relative . extrema. If a function’s derivative is . 5.1. Accumulating Change: Introduction to results of change. Accumulated Change. If the rate-of-change function f’ of a quantity is continuous over an interval a<x<b, the accumulated change in the quantity between input values of a and b is the area of the region between the graph and horizontal axis, provided the graph does not crosses the horizontal axis between a and b. . The Product Rule. The derivative of a product of functions is NOT the product of the derivatives. . If . f. and . g. . are both differentiable, . then:. In other words, the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.. La gamme de thé MORPHEE vise toute générations recherchant le sommeil paisible tant désiré et non procuré par tout types de médicaments. Essentiellement composé de feuille de morphine, ce thé vous assurera d’un rétablissement digne d’un voyage sur .