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Graph the function f(x)=x+4/x

Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes

Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8]

c=

Notice that if you graph the tangent line to the point (c,f(c)) it is parallel to the secant line.

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  1. so, did you do that, and notice the parallel lines? That means that for some c between 1 and 8,

    f'(x) = (8.5-5)/(8-1)

    So, you need to find c where

    -4/c^2 = 1/2

    Eh? Not possible. Looks like (8,8.5) is not on the curve. Better fix you point and redo the steps.

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