Chapter 2.2, Problem 6E

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
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=xâˆ’1/2 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=y2âˆ’y1x2âˆ’x1

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]=nxnâˆ’1

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=1âˆ’321âˆ’0=âˆ’12

Therefore, the slope of the tangent line is âˆ’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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