Consider the given function and the given interval. f\(x\) = (x – 7)**2 text(, ) [5 text(, ) 11] (a) Find the average value fave of f on the

Question

Consider the given function and the given interval. f\(x\) = (x – 7)**2 text(, ) [5 text(, ) 11] (a) Find the average value fave of f on the given interval. fave = 4 Correct: Your answer is correct. (b) Find c such that fave = f(c). (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes.)

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Katherine 1 month 2021-10-15T21:41:01+00:00 1 Answer 0 views 0

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    2021-10-15T21:42:54+00:00

    a. f has an average value on [5, 11] of

    f_{\rm ave}=\displaystyle\frac1{11-5}\int_5^{11}(x-7)^2\,\mathrm dx=\frac{(x-7)^3}{18}\bigg|_5^{11}=\frac{4^3-(-2)^3}{18}=4

    b. The mean value theorem guarantees the existence of c\in(5,11) such that f(c)=f_{\rm ave}. This happens for

    (c-7)^2=4\implies c-7=\pm2\implies c=9\text{ or }c=5

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45:7+7-4:2-5:5*4+35:2 =? ( )