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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