Today in Calculus Go over homework Average Rate of Change (aka slope)

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Presentation transcript:

Today in Calculus Go over homework Average Rate of Change (aka slope) Tangent Lines Homework

Even Answers 12a) Yes, f(1)=1 b) Yes, c, d, e: No Everywhere in[-1,3) except x =0,1,2 Reassign f(1)=2 based on the limit 24. 1,2; x=2 removable 26.

Average Rate of Change The average rate of change of a quantity over a period of time is the amount of change divided by the time it takes. In general: average rate of change of a function over an interval is the amount of change divided by the length of the interval. Example: Find the average rate of change of f(x)=x3 – x over the interval [2,4] Example: Find the average rate of change of f(x)=4x2 – 6x over the interval [1,3]

Example If y = 2x2, find the slope of the curve and the equation of the line tangent to the curve at x = 3

Example If , find the slope of the curve and the equation of the line tangent to the curve at x = 2 Find the slope of f(x) at x = 7, x = -3. At what point is the slope of the tangent line -.25? At what point is the tangent line horizontal?

Homework Pg 87-88: 1-6, 9-10(a & b only)