9514 1404 393
Answer:
- 0.6 → -13.33333
- 0.51 → -15.68628
- 0.4 → -20.00000
- 0.49 → -16.32653
- 0.50 ⇒ -16
Step-by-step explanation:
For repetitive tedious calculations, it is convenient to let a spreadsheet or graphing calculator do them. The slope of the secant line is ...
m = Δy/Δx = (4/x -8)/(x -1/2)
The attachment shows the table of values, along with the average of secant slopes much nearer the point of interest. That seems to suggest a suitable guess for the slope at x = 0.5 is -16.
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Additional comment
For y = 4/x, the derivative is y' = -4/x². The value of this at x = 1/2 is -16.
