Clicker Question 1 What is the instantaneous rate of change of f (x ) = ln(x ) at the point x = 1/10? A. 1/10 B. 10 C. 0 D. ln(1/10) E. undefined

Clicker Question 2 What is the slope of the tangent line to the curve y = x 3/2 at the point x = 9 ? A. 9/2 B. 27 C. 3 D. 9/4 E. 3/2

Clicker Question 3 What is an equation of the secant line connecting (2, f (2)) and (3, f (3)) for the function f (x ) = x 3 ? A. y = 19x 3 B. y = 19x – 30 C. y = -19x + 46 D. y = (1/19)x – 7 E. y = 19x + 30

Clicker Question 4 What is an equation of the tangent line at the point (2, f (2)) for the function f (x ) = x 3 ? A. y = 8x – 8 B. y = 12x 3 – 16 C. y = 12x – 16 D. y = 12x – 20 E. y = 8x – 16

What do we know? (11/9/11) What limits are, how to see them on a graph, and how to (try to) compute them algebraically. Distinguish between limits which are two-sided, one-sided, infinite, at infinity, and non-existent.

What else? To distinguish between the average rate of change of a function between two points (pre- calculus) and the instantaneous rate of change at one point (calculus!). Know the definition and idea of the derivative of a function. Use the definition to compute derivatives algebraically given the function’s formula, or graph them given the function’s graph.

And what else? Know the derivative functions of the most basic elementary functions: All power functions (using the Power Rule) The sin, cos and tan trig functions The natural exponential and log functions (i.e., e x and ln(x ))

Some things we don’t yet know How to compute the derivatives of combinations of functions (i.e., sums, differences, products, quotients, compositions, and inverses. How to apply the derivative to various kinds of “real-life” problems. How to reverse the derivative process (“anti-derivatives”).

Assignment Friday’s class is optional (no attendance, no clickers). Optional worksheet on derivatives is handed out. Test #2 is Monday (11/14).