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A function is given. determine the average rate of change of the function between the given values of the variable. f(x) = 3 − x2; x = 2, x = 2 + h

Respuesta :

tramserran

Average rate of change is SLOPE: m = (y₂ - y₁)/(x₂ - x₁)

f(2) = 3 - (2)²

    = 3 - 4

    = -1

coordinate: (2, -1)

f(2 + h) = 3 - (2 + h)²

           = 3 - (4 + 4h + h²)

           = -h² - 4h - 1

coordinate: (2 + h, h² + 4h - 1)

m = (y₂ - y₁)/(x₂ - x₁)  = (-1 - (h² - 4h - 1)/(2 - (2 + h))  = (-h² + 4h)/-h = h - 4

Answer: h - 4

 

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