Consider the function f(x) = = √x and the point P(4, 2) on the graph f. (a) Graph f and the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 3, 6, and 7. Find the slope of each secant line. (Round your answers to three decimal places.) line passing through Q(3, f(x)) line passing through Q(6, f(x)) line passing through Q(7, f(x)) (b) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4, 2).

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 8T
icon
Related questions
Question

Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4, 2).

The only question that I need answered.

Consider the function f(x)=√x and the point P(4, 2) on the graph f.
(a) Graph fand the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 3, 6, and 7.
Find the slope of each secant line. (Round your answers to three decimal places.)
line passing through Q(3, f(x))
line passing through Q(6, f(x))
line passing through Q(7, f(x))
(b) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4, 2).
Describe how to improve your approximation of the slope.
Choose secant lines that are nearly vertical.
O Define the secant lines with points closer to P.
O Define the secant lines with points farther away from P.
O Choose secant lines that are nearly horizontal.
Transcribed Image Text:Consider the function f(x)=√x and the point P(4, 2) on the graph f. (a) Graph fand the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 3, 6, and 7. Find the slope of each secant line. (Round your answers to three decimal places.) line passing through Q(3, f(x)) line passing through Q(6, f(x)) line passing through Q(7, f(x)) (b) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4, 2). Describe how to improve your approximation of the slope. Choose secant lines that are nearly vertical. O Define the secant lines with points closer to P. O Define the secant lines with points farther away from P. O Choose secant lines that are nearly horizontal.
Expert Solution
steps

Step by step

Solved in 5 steps with 1 images

Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL