Question
Asked Oct 14, 2019
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24
Find the tangent line to y
2
x^ -x+ 2 at x=2.
2
The tangent line to y x-x + 2 at x = 2 is y=
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24 Find the tangent line to y 2 x^ -x+ 2 at x=2. 2 The tangent line to y x-x + 2 at x = 2 is y=

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Expert Answer

Step 1

We first have to find y at x=2

y=2

у3Vx*-х+2
22-2+2
у-
у34
У-2
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у3Vx*-х+2 22-2+2 у- у34 У-2

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Step 2

We need slope dy/dx at x=2 and y=2

First square both sides of the given expression 

then differentiat...

y=/x2-x+2
y2x2-+2
d
(y2)
dx
dx
- (x2-x+2)
dy
2у -2х-1
dx
dy
=2(2)-1
2(2)
dx
dy
4 4-1
dx
dy
4
=3
dx
dy
3
4
dx
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y=/x2-x+2 y2x2-+2 d (y2) dx dx - (x2-x+2) dy 2у -2х-1 dx dy =2(2)-1 2(2) dx dy 4 4-1 dx dy 4 =3 dx dy 3 4 dx

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