The table shows the temperature in degrees Celsius at various distances, d in feet, from a specified point. Estimate the slope of the tangent line at and interpret the result.
A) The temperature is increasing 4.67 per foot at the point 2 feet from the specified point.
B) The temperature is decreasing 0.33 per foot at the point 2 feet from the specified point.
C) The temperature is decreasing 3 per foot at the point 2 feet from the specified point.
D) The temperature is increasing 20 per foot at the point 2 feet from the specified point.

Question

The table shows the temperature in degrees Celsius at various distances, d in feet, from a specified point. Estimate the slope of the tangent line at  and interpret the result. 
A) The temperature is increasing 4.67 per foot at the point 2 feet from the specified point. 
B) The temperature is decreasing 0.33 per foot at the point 2 feet from the specified point. 
C) The temperature is decreasing 3 per foot at the point 2 feet from the specified point. 
D) The temperature is increasing 20 per foot at the point 2 feet from the specified point.

Quizplus · Accepted Answer

To estimate the slope of the tangent line at 11eaa948_cd52_b364_84bc_4d3d10b72059_TB2342_11, we need to find the rate of change of temperature with respect to distance at d=2. Looking at the table, we can see that the temperature changes from 14 to 11 degrees Celsius over a distance of 2 feet, so the slope of the secant line is (11-14)/(2-0)=-3/2. The slope of the tangent line is the limit of this as the distance between the two points approaches zero, which gives us an estimate of the instantaneous rate of change. Therefore, the correct answer is C, which says that the temperature is decreasing 3 degrees Celsius per foot at the point 2 feet from the specified point.

The Table Shows the Temperature in Degrees Celsius at Various