Q. 19 - Calculus

Question

Make a copy of the graph of f used in Exercises 11 and 13, and sketch additional secant lines to illustrate that as $h\to 0$ (or equivalently, as $z\to c$) the slopes of the secant line get closer and closer to the slope of the tangent line to f at $x=c$.

Step-by-Step Solution

Answer

From the graph with many secant lines, we can observe that, as $h\to 0$ for the secant lines, the slope of the secant lines is getting closer and closer to the tangent of the function.

Step 1. Given Information.

The graph of the function.

Step 2. Draw some secant lines.

Draw some secant lines on the function.

Step 3. Observe the graph.

From the graph, we can conclude that as $h\to 0$ for the secant lines, the slope of the secant lines is getting closer and closer to the tangent of the function.