lovelysoul6992 lovelysoul6992
  • 04-02-2018
  • Mathematics
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Find the numbers b such that the average value of f(x) = 15x2 − 42x + 6 on the interval [0, b] is equal to 2.

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sqdancefan
sqdancefan sqdancefan
  • 08-02-2018
The average value (a) of f(x) on the interval [0, b] is given by
[tex] a= \frac{1}{b} \int\limits^b_0 {(15x^{2}-42x+6)} \, dx = 5b^{2} -21b +6[/tex]
You want this value equal to 2, so you have
[tex] 5b^{2} -21b +6 = 2 [/tex]
[tex] (5b-1)(b-4)=0 [/tex]

The values of b are 0.2 and 4.
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