An equation of the tangent plane to the surface $\sqrt { x } + \sqrt { y } + \sqrt { z } = 4$ at (1, 1, 4) is

A) $2 x - 2 y + z = 8$
B) $2 x + 2 y + z = 8$
C) $2 x + 2 y - z = 8$
D) $2 x - 2 y - z = 8$
E) $- 2 x + 2 y + z = 8$

Question

An equation of the tangent plane to the surface $\sqrt { x } + \sqrt { y } + \sqrt { z } = 4$ at (1, 1, 4) is

A) $2 x - 2 y + z = 8$
B) $2 x + 2 y + z = 8$
C) $2 x + 2 y - z = 8$
D) $2 x - 2 y - z = 8$
E) $- 2 x + 2 y + z = 8$

Quizplus · Accepted Answer

The gradient of the function $f(x, y, z) = \sqrt{x} + \sqrt{y} + \sqrt{z}$ at (1, 1, 4) is $(\frac{1}{2}, \frac{1}{2}, \frac{1}{4})$. The equation of the tangent plane is $\frac{1}{2}(x-1) + \frac{1}{2}(y-1) + \frac{1}{4}(z-4) = 0$, which simplifies to $2x + 2y + z = 8$.

An Equation of the Tangent Plane to the Surface x+y+z=4\sqrt { x } + \sqrt { y } + \sqrt { z } = 4x​+y​+z​=4

An Equation of the Tangent Plane to the Surface $\sqrt { x } + \sqrt { y } + \sqrt { z } = 4$