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find an equation for the tangent line to the curve atthe given point. Then sketch the curve and tangent line together. y = (x - 1)2 + 1, (1, 1)

find an equation for the tangent line to the curve atthe given point. Then sketch the curve and tangent line together. y = (x - 1)2 + 1, (1, 1)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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find an equation for the tangent line to the curve at
the given point. Then sketch the curve and tangent line together. y = (x - 1)2 + 1, (1, 1)

Expert Solution
Step 1

Given- y=x-12+1

To find- the equation of the line which is tangent to the given curve.

Using concpet- To find the slope of the line, differentiate the above function w.r.t x  and substitute the given point and to find the equation of the tangent line use the formula as slope=y-y1x-x1.

Step 2

Explanation- Rewrite the given function,

y=x-12+1

Now, differentiate the above function, w.r.t. x , we get,

dydx=2·x-1·ddxx-1+0     =2·x-1·1     =2x-2

Now as we have to find the value of slope at the point 1,1, so the slope is,

dydx1,1=2·1-2           =2-2           =0

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