### Day 16 - Tangent Line - 09.09.14

 Bell Ringer"Confuse Students to Help Them Learn"If f(x) = 2x - 5, find f(x + h)2x + 2h - 52x - 2h - 5-2x + 2h + 5-2x + 2h - 5none of the aboveFind the slope of the tangent line of f(x) at any point x.-22-2x2xnone of the aboveIf f(x) = -2x2 + 4x - 1, find f(x + h)-2x2 - 4hx - 2h2 + 4x + 4h - 12x2 - 4hx - 2h2 + 4x + 4h - 1-2x2 + 4hx - 2h2 + 4x + 4h - 12x2 - 4hx - 2h2 + 4x + 4h + 1none of the aboveFind the slope of the tangent line of f(x) at any point x.-4x4x-44none of the aboveReviewEquation of Secant LineEquation of Tangent LineLessonDrawing the Tangent Line on a GraphDerivativeSlope of a Vertical Tangent LineDifferentiation and ContinuityTangent Line Practicepage 103 #1-3 (odds)page 103 #5-9 (odds)page 103 #10Checkpoint #1page 103 #25-31 (odds)page 103 #32Checkpoint #2page 103 #33-37 (odds)page 103 #38Checkpoint #3page 103 #39-41 (odds)page 103 #42Checkpoint #4Derivativepage 103 #11-23 (odds)page 103 #24Checkpoint #5Exit TicketAnswer the problem that will be posted at the end of the block. Lesson Objective(s)How can tangent lines be drawn for points on a function?How is the derivative related to tangent lines?How are differentiation and continuity related?Standard(s)APC.5Investigate derivatives presented in graphic, numerical, and analytic contexts and the relationship between continuity and differentiability.The derivative will be defined as the limit of the difference quotient and interpreted as an instantaneous rate of change.APC.6​The student will investigate the derivative at a point on a curve.Includes:finding the slope of a curve at a point, including points at which the tangent is vertical and points at which there are no tangentsusing local linear approximation to find the slope of a tangent line to a curve at the point​defining instantaneous rate of change as the limit of average rate of changeapproximating rate of change from graphs and tables of values.APC.7Analyze the derivative of a function as a function in itself.Includes:comparing corresponding characteristics of the graphs of f, f', and f''​defining the relationship between the increasing and decreasing behavior of f and the sign of f'​translating verbal descriptions into equations involving derivatives and vice versaanalyzing the geometric consequences of the Mean Value Theorem;defining the relationship between the concavity of f and the sign of f "; and​identifying points of inflection as places where concavity changes and finding points of inflection.Mathematical Practice(s)#1 - Make sense of problems and persevere in solving them#2 - Reason abstractly and quantitatively#3 - Construct viable arguments and critique the reasoning of others