Estimate the instantaneous rate of change for g(x) = 2/(x+6).

Question

Estimate the instantaneous rate of change for the function g(x) = 2/(x+6) at the point where x = 3.

Use a TI-83 (or 84) to calculate the slopes of secant lines as x gets close to 3. Use the table feature of the TI-83.

Answer 1

g(x) = 2/(x+6)

g'(x) = -2/(x+6)^2

g'(3) = -2/81 = instantaneous rate of change when x=3

= limit of the secant line slope as endpoints of the secant line get increasingly close together

= about -.0247

= -2/9 divided by 9

= -.222.../9

= -.0246914...

= slope of a rectangular hyperbola when x=3

which is nearly flat in the top right branch of the hyperbola, nearly zero, but negative as it slopes downward approaching zero

Answer 2

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