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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.6, Problem 1E

**(a)**

To determine

**To write:** The slope of the secant line through the points

Expert Solution

The slope of the secant line through the points

**Given:**

The equation of the curve

The slope of the secant line through the points

**Formula used:**

The slope of the secant line through the points

**Calculation:**

Obtain the slope of the secant line through the points

Substitute 3 for *a* in equation (1),

Thus, the slope of the secant line

(b)

To determine

**To write:** The slope of the tangent line at *P*.

Expert Solution

The slope of the tangent line at *P* is

**Given:**

The equation of the curve

The slope of the secant line through the points

**Formula used:**

The slope of the tangent line at the point

**Calculation:**

The slope of the tangent line at the point *P* is the limit of the slope of the secant line *PQ* as *Q* approaches *P.*

From part (a), the slope of the secant line at *PQ* is,

Substitute

Thus, the slope of the tangent line at the point *P* is *.*