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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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