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. 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”. Section 3.1b. Remember, that in . graphical terms. , the derivative of a. function at a given point can be thought of as the . slope. of the curve at that point…. Therefore, we can get a good idea of what the graph of. Derivative. A . derivative. of a function is the instantaneous rate of change of the function at any point in its domain.. We say this is the derivative of . f. with respect. to the variable . x. .. 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. We will learn about:. Concavity -Points of Inflection - The Second Derivative Test. Review. If a functions wants to switch from decreasing to increasing. or visa versa, what are its options of approach/attack! (There is only three options). Derivative. A . derivative. of a function is the instantaneous rate of change of the function at any point in its domain.. We say this is the derivative of . f. with respect. to the variable . x. .. 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 . -More Effort Needed!. -Wording of Problems (derivative, slope at a point, slope of tangent line…). -Product / Quotient Rules!!!. -Quiz . I:g. and . II:a. -Weekly 7 , 8 , 10 . The Chain Rule. 4.1.1. 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 . Lengths of Curves. Length of a Smooth Curve. Note: This method only works with a function that has a continuous. f. irst derivative – this property is called . smoothness. . A function with. a. continuous first derivative is . Slope of the Tangent Line. If . f. is defined on an open interval containing . c. and the limit exists, then . . and the line through (. c. , . f. (. c. )) with slope . m. is the line tangent to the graph of . 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.. The Second Derivative and the Function. The first derivative tells us where a function is increasing or decreasing. But how can we tell the manner in which a function is increasing or decreasing?. For example, if . NOW: . Replace: . Graph of . , with words:. Graph: (. , the . slope of the tangent line to the . function . . at that . point). .  . CALCULUS problem:. Graph: (. , the slope of the tangent line to the function .