Section 2.1 The Tangent and Velocity Problems Making the simple complicated is commonplace; making the complicated simple, awesomely simple, that's creativity.--Charles Mingus

Example 1 (Given a function) Find an equation of the tangent line to the parabola at the point .

Example 2 (Table/Graph) The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off). Use the data to draw the graph of this function and estimate the slope of the tangent line where . [Note: The slope of the tangent line represents the electric current flowing from the capacitor to the flash bulb (measured in microamperes).]

Example 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of the ball after 5 seconds.

Instantaneous Velocity: The limiting value of these average velocities over shorter and shorter time periods that start at