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bogdanovich [222]
3 years ago
12

Consider the given function and the given interval.

Mathematics
1 answer:
docker41 [41]3 years ago
7 0

Answer:

  (a)  fave = 8

  (b)  c = 64/9

  (c)   c ≈ 7.111

Step-by-step explanation:

(a) The average value of the function is its integral over the interval, divided by the width of the interval.

  f_{ave}=\displaystyle\frac{1}{16-0}\int_0^{16} {3x^{\frac{1}{2}}} \, dx=\left.\frac{x^{3/2}}{8}\right|_0^{16}=8

__

(b) We want ...

  f(c) = 8

  3√c = 8 . . . . . use f(c)

  √c = 8/3 . . . . . divide by 3

  c = (8/3)² . . . . square

  c = 64/9

__

(c) c ≈ 7.111

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