Unit 5: Derivatives 4.1 The Derivative Function Equations of Tangents and Normals State what the derivative represents (3 Find the equation of the tangent: interpretations) To a curve at a given point. determine expression for from first principles Parallel to a given line evaluate at = a x Find the equation of a normal to a curve Differentiability Find points on a curve where the tangent has a sketch the graph of the derivative, using the given slope. slopes of the tangent lines at various places on the curve of f. 4.4 The Quotient Rule Distinguish between continuity and the quotient rule. differentiability. Apply the quotient rule. Determine whether a function is differentiable at Find the equation of a given tangent x = a: algebraically or graphically. Find points on the graph where the tangent has a given slope. 4.2 Derivatives of Polynomial Functions 4.6 The Derivative of a composite Function Derivative Rules: Constant, Constant Multiple, differentiate composite functions the Chain Power, Sum and Difference Rule and power-product-quotient-chain rules Be able to state and apply the rules combined Newton’s Method: 4.3 The Product Rule differentiate composite functions using the state and prove the product rule. Apply the Chain Rule product rule Leibniz’s Method: the power of a function rule Unit6: Applications of Derivatives 1. 5.2 Higher-Order Derivatives, Velocity, and 3. 5.5 - 5.6 Optimization Problems Acceleration apply problem solving steps to maximizing and Find higher order derivatives minimizing problems involving: area, volume, use position function s(t), to problems geometry, economics, social sciences and involving velocity and acceleration using the science fact that: 4. The Derivatives of the Sine and Cosine Functions 2. 5.4 Maximum and Minimum on an Interval Know the derivatives of the sine and cosine Extreme values on a closed interval function. using conditions set to find critical numbers and apply the derivatives of sine/cosine functions to function values at the endpoints of an interval to differentiate other related functions. determine the extrema (max./min. values) on that interval 5. Applications of Trigonometric Function apply to graphs and problem solving solve rate of change problems and applications involving trigonometric functions.
Unit 5: Derivatives 4.1 The Derivative Function State what the derivative represents (3 interpretations) determine expression for from first principles evaluate at x = a Differentiability sketch the graph of the derivative, using the slopes of the tangent lines at various places on the curve of f. Distinguish between continuity and differentiability. Determine whether a function is differentiable at x = a: algebraically or graphically. 4.2 Derivatives of Polynomial Functions Derivative Rules: Constant, Constant Multiple, Power, Sum and Difference Be able to state and apply the rules 4.3 The Product Rule state and prove the product rule. Apply the product rule the power of a function rule Equations of Tangents and Normals Find the equation of the tangent: To a curve at a given point. Parallel to a given line Find the equation of a normal to a curve Find points on a curve where the tangent has a given slope. 4.4 The Quotient Rule the quotient rule. Apply the quotient rule. Find the equation of a given tangent Find points on the graph where the tangent has a given slope. 4.6 The Derivative of a composite Function differentiate composite functions the Chain Rule and power-product-quotient-chain rules combined Newton’s Method: differentiate composite functions using the Chain Rule Leibniz’s Method: Unit6: Applications of Derivatives 1. 5.2 Higher-Order Derivatives, Velocity, and Acceleration Find higher order derivatives use position function s(t), to problems involving velocity and acceleration using the fact that: 2. 5.4 Maximum and Minimum on an Interval Extreme values on a closed interval using conditions set to find critical numbers and function values at the endpoints of an interval to determine the extrema (max./min. values) on that interval apply to graphs and problem solving 3. 5.5 - 5.6 Optimization Problems apply problem solving steps to maximizing and minimizing problems involving: area, volume, geometry, economics, social sciences and science 4. The Derivatives of the Sine and Cosine Functions Know the derivatives of the sine and cosine function. apply the derivatives of sine/cosine functions to differentiate other related functions. 5. Applications of Trigonometric Function solve rate of change problems and applications involving trigonometric functions.
Calculus%20Review%20Outline%20June%202015.docx