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1. Suppose that the point A(4, 2) lies on the curve g(x)=√x and that B is another point on that curve where B can be generally represented as (x,√x). a) Complete the following table by finding the slope of the secant line AB (correct to six decimal places). B Slope of Secant Line AB B Slope of Secant Line AB 5 3 4.5 3.5 4.1 3.9 4.001 3.999 b) Using the results obtained in (a), guess the value of the slope of the tangent line to the curve at point A(4, 2). c) Differentiate g(x) and evaluate it at x = 4. What can be concluded from your answers in (b) and (c)? e) Do you think the function g(x) is differentiable for all x ≥ 0? Explain your answer.

1. Suppose that the point A(4, 2) lies on the curve g(x)=√x and that B is another point on that curve where B can be generally represented as (x,√x). a) Complete the following table by finding the slope of the secant line AB (correct to six decimal places). B Slope of Secant Line AB B Slope of Secant Line AB 5 3 4.5 3.5 4.1 3.9 4.001 3.999 b) Using the results obtained in (a), guess the value of the slope of the tangent line to the curve at point A(4, 2). c) Differentiate g(x) and evaluate it at x = 4. What can be concluded from your answers in (b) and (c)? e) Do you think the function g(x) is differentiable for all x ≥ 0? Explain your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose that the point A(4, 2) lies on the curve g(x)=√x and that B is another point on that curve where B can be generally represented as (x,√x). a) Complete the following table by finding the slope of the secant line AB (correct to six decimal places). B Slope of Secant Line AB B Slope of Secant Line AB 5 3 4.5 3.5 4.1 3.9 4.001 3.999 b) Using the results obtained in (a), guess the value of the slope of the tangent line to the curve at point A(4, 2). Differentiate g(x) and evaluate it at x = 4. d) What can be concluded from your answers in (b) and (c)? e) Do you think the function g(x) is differentiable for all x ≥ 0? Explain your answer.
Transcribed Image Text:1. Suppose that the point A(4, 2) lies on the curve g(x)=√x and that B is another point on that curve where B can be generally represented as (x,√x). a) Complete the following table by finding the slope of the secant line AB (correct to six decimal places). B Slope of Secant Line AB B Slope of Secant Line AB 5 3 4.5 3.5 4.1 3.9 4.001 3.999 b) Using the results obtained in (a), guess the value of the slope of the tangent line to the curve at point A(4, 2). Differentiate g(x) and evaluate it at x = 4. d) What can be concluded from your answers in (b) and (c)? e) Do you think the function g(x) is differentiable for all x ≥ 0? Explain your answer.
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