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Find the slope of the line tangent to the graph of x²+2xy² +3y=31 at the point (2, -3)​

User MBo
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1 Answer

3 votes

9514 1404 393

Answer:

22/21

Explanation:

Taking the derivative, we have ...

2x·dx +2y²·dx +4xy·dy +3·dy = 0

dx(2x +2y²) +dy(4xy+3) = 0

At the given point, this is ...

dx(2·2 +2·(-3)²) +dy(4·2·(-3) +3) = 0

22dx -21dy = 0

dy/dx = 22/21

The slope of the tangent at the point of interest is 22/21.

Find the slope of the line tangent to the graph of x²+2xy² +3y=31 at the point (2, -3)​-example-1
User Vishal Panara
by
5.3k points
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