C Roettger, Fall 14
Math 265 Quiz 6D – Solutions
Graph of f (x, y) in blue, tangent plane red. Intersection curves of the graph
with planes x = x0 and y = y0 green and yellow, respectively.
Problem 1 Consider the function
f (x, y) =
x2 + xy
.
3
Find an equation for the tangent plane to the graph of f at P0 = (2, −1).
Solution. First, the partial derivatives
∂f
2x + y
=
∂x
3
∂f
x
=
.
∂y
3
At P0 , these have the values 1 and 2/3, respectively. Finally, we need the
value f (P0 ) = 2/3. So the tangent plane to the graph of f at P0 is described
by the equation
z=
2
2
2
2
+ (x − 2) + (y + 1) = − + x + y.
3
3
3
3