Exercise · ZW-TANGENT-PLANE-007 · ★★☆ Intermediate
At which point \((a,b)\) is the tangent plane to \(z=x^2+y^2-2x+4y\) horizontal?
Choose one option.
Show answer
- B. \((1,-2)\)
Explanation
It is horizontal when \(f_x=2x-2=0\) and \(f_y=2y+4=0\), that is, at \((1,-2)\).
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.
\[z=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\]
More practice problems: tangent plane
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- ZW-TANGENT-PLANE-004 Find the tangent plane to z=√x^2+y^2 at the point (3,4,5).
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