2.6.  Tangents, Velocities and Other Rates of Change

objective: to be able to determine average rates of changes graphically, algebraically, and numerically
to be able to determine instantaneous rates of changes graphically, algebraically, and numerically
to be able to find the equation of the tangent to a function at a given point

key ideas and/or vocabulary

• secant lines, tangent lines, average rate of change, instantaneous rate of change, displacement functions,  average velocity, instantaneous velocity,  average rate of change of y with respect to x over an interval
• definition of tangent line page 143

Equation 2. 

• equation for secant line and tangent line given arbitrary points, #1
• find slope of tangent line by choosing two points on tangent line by taking limits
• find equation of the tangent line
• zoom in to see what appears to be a straight line
• using the definition of tangent and equation 2, #5
• finding equation of tangent line, #8

• position function - displacement
• average and instantaneous velocity 
• understanding the position function graphically, #13
• instantaneous velocity algebraically, #15.

• average rate of change of y with respect to x over an interval
• instantaneous rate of change = 
• estimating rates of change from data, #21

QUESTION OF THE DAY

Find

SOLUTION

SOLUTION.