Exercise · ZW-TANGENT-PLANE-001 · ★☆☆ Basic
Find the tangent plane to \(z=x^2+y^2\) at the point \((1,2,5)\).
Choose one option.
Show answer
- A. \(z=2 x + 4 y - 5\)
Explanation
\(f_x=2x=2\) and \(f_y=2y=4\) at \((1,2)\), so \(z=5+2(x-1)+4(y-2)=2x+4y-5\).
Review the concept: Tangent plane
The tangent plane to the graph of a function \(f(x,y)\) at the point \((a,b,f(a,b))\) is the plane that best approximates the surface near that point and contains the tangent lines of its two coordinate sections.
\[z=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\]
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