Write an equation of the tangent line to the curve f (x) = 2// + 3x at the point (4, f (4)). Upload your paper in the next question. The slope of the tangent line, rounded to the nearest hundredth, is

Write an equation of the tangent line to the curve f (x) = 2// + 3x at the point (4, f (4)). Upload your paper in the next question. The slope of the tangent line, rounded to the nearest hundredth, is

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 3E

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Expert Solution

Step 1

Here, the given equation of the curve is:

$f (x) = \frac{2}{\sqrt{x}} + 3 x$

To find the slope and the equation of the tangent line to the curve at $(4, f (4)) i . e . (4, 13)$

because $f (4) = \frac{2}{\sqrt{4}} + 3 (4) = \frac{2}{2} + 12 = 1 + 12 = 13$

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