Problem 891

Estimate the slope (in y-units per x-unit) of the tangent line to the curve.





First look at the tangent line on the curve.

When moving from left to right the line decreases.

Therefore the slope of the line will be negative.

The slope of a line L is defined as

sloe = \frac{rise}{run}= \frac{y-y_{o}}{x-x_{o}}

where (x,y) and (x_{0},y_{0}) are points on the line.

To estimate the slope, start at any point (x_{0},y_{0}) on the line and move one unit to the right on the x-axis. Estimate the new value yo of the line at x = xo + 1. The slope will be the difference y – y0.

If we start at xo = 7 we can estimate that y0 \approx 6.

Now we move 1 unit to the right on the x-axis to x = 8.

At x = 8 we estimate that y\approx 0.


slope \approx  \frac{y-y_{o}}{x-x_{o}} \approx  \frac{0-6}{8-7} \approx  -6




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