1. One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at.

1. One of
the fundamental themes of calculus is to find the slope of the tangent line to
a curve at a point. To see how this can be done, consider the point on the
graph of the quadratic function which is shown in the figure.

(a) Find the slope of the line
joining and Is the slope of the tangent line at greater than or less than the
slope of the line through and

(b) Find the slope of the line
joining and Is the slope of the tangent line at greater than or less than the
slope of the line through and

(c) Find the slope of the line
joining and Is the slope of the tangent line at greater

1. One of
the fundamental themes of calculus is to find the slope of the tangent line to
a curve at a point. To see how this can be done, consider the point on the
graph of the quadratic function which is shown in the figure.

(a) Find the slope of the line
joining and Is the slope of the tangent line at greater than or less than the
slope of the line through and

(b) Find the slope of the line
joining and Is the slope of the tangent line at greater than or less than the
slope of the line through and

(c) Find the slope of the line
joining and Is the slope of the tangent line at greater than or less than the
slope of the line through and

(d) Find the slope of the line
joining and in terms of the nonzero number

(e) Evaluate the slope formula
from part (d) for 1, and 0.1. Compare these values with those in parts (a)(c).

(f ) What can you conclude the
slope of the tangent line at _2, 4_ to be? Explain your answer.

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