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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F746110e2-a72c-4893-8a24-14c8951e5bbe%2F9b97a4f0-ad21-4fe8-a8db-c75c1433aae9%2Fcglbsds_processed.png&w=3840&q=75)
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 -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F746110e2-a72c-4893-8a24-14c8951e5bbe%2F9b97a4f0-ad21-4fe8-a8db-c75c1433aae9%2Fak8gat8_processed.png&w=3840&q=75)
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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