Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q15.

Expert-verified
Precalculus Mathematics for Calculus
Found in: Page 922
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

Find the equation of the tangent line to the curve at the given point. Graph the curve and tangent line.

.y=xx1, at (2,2)

The equation of the tangent line to the curve at a given point isy=x+4 .

The graph of the curve and tangent line:

See the step by step solution

Step by Step Solution

Step 1. Given information.

The function here given is,

y=xx1point=(2,2)

Step 2. Formula used.

The tangent line to the curvey=f(x) at the point P(a,f(a)) is the line through p with slope,

m=limxaf(x)f(a)xa.

provided that this limit exists.

Equation of tangent line:

y=m(xa)+f(a)

Step 3. Finding the slope of tangent line at given point.

Let y=xx1, then the slope of the tangent line at (2,2) is,

m=limx2f(x)f(2)x2=limx2(xx1)(221)x2=limx2xx121x1x1x2=limx2x2x+2x1x2=limx2(x2)(x2)(x1)=121=1

The slope of the tangent line is -1.

Step 4. Finding the equation of the tangent line at a given point.

Here, the slope of the tangent line ism=1 . Equation of the tangent line is written as,

y=1(x2)+2y=x+2+2y=x+4 ,

Therefore, the equation of the tangent line isy=x+4 .

Step 5. Graphing the curve and the tangent line.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.