Question

HELP WITH THIS QUESTION PLEASE

Answer 1

9514 1404 393

Answer:

  about 2.1

Step-by-step 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.