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Semmy [17]
3 years ago
5

The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

Mathematics
1 answer:
arlik [135]3 years ago
7 0
Y^3x + y^2x^2 = 6 

<span>Using implicit differentiation </span>
<span>
3 y^2.y'.x+y^3+2 y.y'.x^2+2 y^2.x=0
 </span>
<span>y'(3 y^2.x+2 y. x^2) = -y^3-2 y^2.x </span>
<span>
y' = -[y^2(y+2 x)]/[x y(3 y+2 x)] </span>
<span>
   = -[y(y+2 x)]/[x(3 y+2 x)] </span>
<span>
Substituting x =2 and y = 1:
 </span>
<span>y' = -(1)(1+4)/[2(3+4)] </span>
<span>   = -5/14 </span>

<span>The slope of the tangent of the curve at (2,1) will be:
 m = -5/14</span>
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Step-by-step explanation:

Solution by substitution method

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Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

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⇒y=(128-115)/23

⇒y=13/23

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Step-by-step explanation:

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Angelina_Jolie [31]

Answer:

Step-by-step explanation:

In this particular case we have the following system of equations:

y

=

−

3

x

+

4

[

E

q

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1

]

x

+

4

y

=

−

6

[

E

q

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2

]

Substituting

[

E

q

.

1

]

in

[

E

q

.

2

]

:

x

+

4

(

−

3

x

+

4

)

=

−

6

Applying the distributive property on the left side:

x

−

12

x

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−

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x

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22

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:

x

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−

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Substituting

x

=

2

in

[

E

q

.

1

]

:

y

=

−

3

(

2

)

+

4

=

−

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Therefore

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SVETLANKA909090 [29]

Answer:

a

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