Math (Secant Lines)

Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f?

-Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5.

-Find the slope of each secant line

-Use the results to estimate the slope of the tangent line to the function at p(4,2). Describe how to improve your approximation of the slope?

I already graphed the function with the x values for 1, 3, and 5 but I'm confused on how to do the rest. Any help is greatly appreciated!

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  1. So far I tried to figure out the slope of each secant line:

    For x=1 the slope is 1/3
    For x=3 the slope is 2-sqrt(3)
    For x=5 the slope is sqrt(5)-2

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  2. Any ideas?

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  3. the slopes look good.

    The secant through (1,1) doesn't help much, but the lines through (3,√3) and (5,√5) bracket the tangent at (4,2).

    Pick points closer to (4,2) to refine your value.

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