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Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 6x – 5Vx, (1, 1)

Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 6x – 5Vx, (1, 1)

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter4: Graphs
Section4.6: Find The Equation Of A Line
Problem 4.129TI: Find an equation of a line parallel to the line y=3x+1 that contains the point (4,2) . Write the...
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Step 3 Now since 1-1/2 = 1 we have the following. m = f '(1) -5/2 Submit Skip (you cannot come back)
Transcribed Image Text:Step 3 Now since 1-1/2 = 1 we have the following. m = f '(1) -5/2 Submit Skip (you cannot come back)
Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 6x - 5/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y - Yo = m(x - xo). This means that we need to find the slope m of the line and a point (xo, Yo) on the line. We begin by finding the slope. The line tangent to f(x) at (xo, Yo) will have the slope m = f '(xo). We have y = f(x) = 6x – 5/x. Since 5Vx = 5x1/2, then -1/2 f '(x) = 6 Step 2 Using f '(x) = 6 - we can now find the slope of the tangent line at (1, 1) by finding the following. m = f 1 -1/2 = 6 -
Transcribed Image Text:Find the equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 6x - 5/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y - Yo = m(x - xo). This means that we need to find the slope m of the line and a point (xo, Yo) on the line. We begin by finding the slope. The line tangent to f(x) at (xo, Yo) will have the slope m = f '(xo). We have y = f(x) = 6x – 5/x. Since 5Vx = 5x1/2, then -1/2 f '(x) = 6 Step 2 Using f '(x) = 6 - we can now find the slope of the tangent line at (1, 1) by finding the following. m = f 1 -1/2 = 6 -
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