Let f(x) = x2. Use a calculator to construct a table of the slopes of the secant lines
for f on the intervals [2:9; 3], [2:99; 3]; [2:999; 3]; [2:9999; 3]; [3; 3:1]; [3; 3:01]; [3; 3:001], and [3; 3:0001]. Record the slopes to ve decimal places. Use that data to guess the slope of
the line tangent to the graph of f at x = 3. Finally, write down the equation of that
tangent line.

Question

Let f(x) = x2. Use a calculator to construct a table of the slopes of the secant lines
for f on the intervals [2:9; 3], [2:99; 3]; [2:999; 3]; [2:9999; 3]; [3; 3:1]; [3; 3:01]; [3; 3:001], and [3; 3:0001]. Record the slopes to ve decimal places. Use that data to guess the slope of
the line tangent to the graph of f at x = 3. Finally, write down the equation of that
tangent line.

anonymous · Answer

I came up with the slope being 6, with a final answer of f(x) = 6x - 9.