   Chapter 2.2, Problem 6E

Chapter
Section
Textbook Problem

Estimating Slope In Exercises 5 and 6, use the graph to estimate the slope of the tangent line to y = x n at the point (1.1). Verify your answer analytically. To print an enlarged copy of the graph, go to Math Graph. com.(a) y = x − 1 / 2 (b) y = x − 1 (a)

To determine

To calculate: The slope of the tangent line to y=x1/2 at the point (1,1) by using the provided graph and verify the answer analytically.

Explanation

Given:

The function is: y=x1/2 which has the graph provided below,

Formula used:

The slope of the line passing through the points (x1,y1) and (x2,y2), is given by,

m=y2y1x2x1

The slope of a graph of a function is the derivative of that function, as below,

m=ddx[f(x)]

The power rule of differentiation states that,

ddx[xn]=nxn1

Calculation:

Consider the graph,

Observe that the tangent line crosses the y-axis at y=32.

So, the y-intercept of the tangent line is (0,32).

The next point is (1,1).

So, the slope of the line passes through the point (0,32) and (1,1) is,

m=13210=12

Therefore, the slope of the tangent line is 12

(b)

To determine

To calculate: The slope of the tangent line to y=x1 at the point (1,1) by using the provided graph and verify the answer analytically.

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