9514 1404 393
Answer:
about 2.1
Explanation:
The slope of the secant line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (121/100 -1)/(11/10 -1) = (21/100)/(1/10) = 2.1
The slope of the tangent is about 2.1.
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Additional comment
We can refine our estimate by choosing a secant line between the points (9/10, 81/100) and (11/10, 121/100). That is, points either side of x=1.
That slope is ...
(121/100 -81/100)/(11/10 -9/10) = (40/100)/(2/10) = 2.0
We expect the slope of the tangent at x=1 to be exactly 2.0.