Find an equation of the tangent plane to the given

Cynthia Bell 2022-01-05 Answered
Find an equation of the tangent plane to the given surface at the specified point.
\(\displaystyle{z}={3}{y}^{{2}}-{2}{x}^{{2}}+{x},{\left({2},-{1},-{3}\right)}\)

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Expert Answer

Lakisha Archer
Answered 2022-01-06 Author has 3772 answers
Solve for the partial derivative of f with rspect to x
\(\displaystyle{{f}_{{x}}{\left({x},{y}\right)}}=-{4}{x}+{1}\)
Now solve for the partial derivative of f with respect to y
\(\displaystyle{{f}_{{y}}{\left({x},{y}\right)}}={6}{y}\)
Evaluate at the point \(\displaystyle{\left({2},-{1}\right)}\)
\(\displaystyle{{f}_{{x}}{\left({2},-{1}\right)}}=-{7}\)
\(\displaystyle{{f}_{{y}}{\left({2},-{1}\right)}}=-{6}\)
Frame the equation of the tangent plane
\(\displaystyle{x}+{3}=-{7}{x}+{14}-{6}{y}-{6}\)
Simplify
\(\displaystyle-{7}{x}-{6}{y}+{5}={z}\)
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