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  • 29-10-2020
  • Mathematics
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What is the average rate of change for the function f(x) = x^3 − 6x^2 + 4x +7 over the interval 0≤x≤5?

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joshlind3
joshlind3 joshlind3
  • 29-10-2020

Answer:

-1

Step-by-step explanation:

The average rate of change of f(x) is slope because

[tex]\frac{\int\limits^b_a {(\frac{d}{dx}f(x)) } \, dx }{b-a}=\frac{f(b)-f(a)}{b-a}[/tex]

so,

[tex]\frac{f(5)-f(0)}{5-0}\\ f(5) = 5^3 - 6(5^2) + 4(5) + 7\\= 2\\f(0) = 7\\\frac{2-7}{5}=\frac{-5}{5}=-1[/tex]

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