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Paladinen [302]
3 years ago
6

Find the tangent plane to the given surface of f(x,y)=6- 6/5 x-y at the point (5, -1, 1). Make sure tat your final answer for th

e plane is in simplified form.
Mathematics
1 answer:
HACTEHA [7]3 years ago
4 0

Answer:

Required equation of tangent plane is z=\frac{6}{5}(x-5y-11).

Step-by-step explanation:

Given surface function is,

f(x,y)=6-\frac{6}{5}(x-y)

To find tangent plane at the point (5,-1,1).

We know equation of tangent plane at the point $(x_0,y_0,z_0)[/tex] is,

z=f(x_0,y_0)+f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)\hfill (1)

So that,

f(x_0,y_0)=6-\frac{6}{5}(5+1)=-\frac{6}{5}

f_x=-\frac{6}{5}y\implies f_x(5,-1,1)=\frac{6}{5}

f_y=-\frac{6}{5}x\implies f_y(5,-1,1)=-6

Substitute all these values in (1) we get,

z=\frac{6}{5}(x-5)-6(y+1)-\frac{6}{5}

\therefore z=\frac{6}{5}(x-5y-11)

Which is the required euation of tangent plane.

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I personally find it more convenient to look for the zeros (x-intercepts) of the difference f(x)-g(x). That way, I'm only graphing one function, and I don't have to look all over the graph to try to find the point of intersection. (The solution is always on the x-axis.) The attached graph shows f(x) - g(x) as a dashed green line.

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