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.
[tex]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[/tex]
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(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
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(c) c ≈ 7.111
