# 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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