Exercise 1087Calculus › Multivariable calculus › Partial derivativesL1Added 3 Nov 2026

Tangent plane to a graph

#tangent plane#differentiability#graph

Statement

Find the tangent plane to the surface $z=x^2+y^2$ at the point $(1,2,5)$ .

Hint

The tangent plane is $z=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)$ .

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Partial derivatives. $f_x=2x$ , $f_y=2y$ ; at $(1,2)$ : $f_x=2$ , $f_y=4$ .

Tangent plane. $z=5+2(x-1)+4(y-2)=2x+4y-5$ .

Conclusion. The tangent plane is $z=2x+4y-5$ .