Unit 3 Learning Outcomes

Upon successful completion of this unit, you will be able to:

• state the definition of a derivative of a function f(x);
• recognize and use the common equivalent notations for the derivative;
• state the graph and rate meanings of a derivative;
• estimate a tangent line slope and instantaneous rate of change from the graph of a function;
• write the equation of the line tangent to the graph of a function f(x);
• calculate the derivatives of the elementary functions;
• calculate second and higher derivatives and state what they measure;
• differentiate compositions of functions using the chain rule;
• calculate the derivatives of functions given as parametric equations and interpret their meanings geometrically and physically;
• state whether a function, given by a graph or formula, is continuous or differentiable at a point or on an interval;
• solve related rate problems using derivatives;
• approximate the solutions of equations by using derivatives and Newton's method;
• approximate the values of difficult functions by using derivatives;
• calculate the differential of a function using derivatives and show what the differential represents on a graph; and
• calculate the derivatives of really difficult functions by using the methods of implicit differentiation and logarithmic differentiation.