Chapter 2.P, Problem 28P

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(a) The cubic function
*f* and its tangent lines at the *average* of each pair of zeros. What do you notice?

(b) Suppose the cubic function
*a, b,* and *c.* Prove, with the help of a computer algebra system, that a tangent line drawn at the average of the zeros *a* and *b* intersects the graph of *f* at the third zero.

To determine

**(a)**

**To sketch:** The graph of f and its tangent lines at the average of each pairs of zeros and to explain what will notice

Explanation

**1) Concept:**

Take the average of each pair of zeros and then draw the tangent line at that point and then conclude.

**2) Given:**

3) **Graph:**

Consider the purple tangent line at

X intercept of this line is at x = 0 which is third zero of the cubic function

Now, consider blue tangent at

<

To determine

**(b)**

**To prove:**

The tangent line drawn at the average of zeros

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