Average Rate vs. Instantaneous Rate

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Presentation transcript:

Average Rate vs. Instantaneous Rate Average Rate of Change Between a and b Instantaneous Rate of Change at a a b

Average Rate of Change Between x = a & x = b f(b) – f(a) b - a = Slope of the line f(b) f(b) – f(a) f(a) b - a a b

Average Rate vs. Instantaneous Rate Average Rate of Change Between a and b Instantaneous Rate of Change at a a b

Instantaneous Rate at x = a Use a =3, h = 0.01 Instantaneous Rate of Change at a f (3.01)- f(3) 3.01 - 3 = f(a+h)=f(3.01) f(3.01)-f(3) f(a)= f(3) 3.01- 3 h= 0.01 a =3 a+h= 3.01

Find: a) f ‘ (1) f (4)- f(3) 4 - 3 b) f (4)- f(3) c) f (4)- f(3) 4 - 3 Average Rate of Change between x=3 and x=4 a) f ‘ (1) f (4)- f(3) 4 - 3 b) f (4)- f(3) c) f (4)- f(3) 4 - 3 f (4)- f(3) Inst. Rate of Change at x = 1 f ‘ (1) f(1) 1 2 3 4

The Constant Rule If f(x) is constant, the derivative is 0. 5 -8 -6 -4 -8 -6 -4 -2 2 4 6 8 -5

The Linear Rule If f(x) is a linear function, the derivative is its own slope. 5 -8 -6 -4 -2 2 4 6 8 -5