Suppose f is a differentiable function of x and y, and g(r, s) = f(7r - s, s² - 2r). Use the table of values below to calculate g,(2, 6) and g,(2, 6). fy 9 7 9,(2, 6) = 9,(2, 6) = (8, 32) (2,6) X f 1 3 9 3 1 fx 4 6

Q: Find the local extreme values of the function: f(x,y)=xy-x^2-y^2-3x-3y+12.

A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.…

A:

Q: Find the interval(s) where the function y = x – 2x² – 7x + 2 is concave down. Justify your answer.

A: Find the double derivative of y and then equate it to zero.

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

A:

Q: For the function f(x,y) = x³ ²xy, find fx and f.

A: Given function:- fx,y=x3e2xy

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: For the function f(x,y) = ³xy, find fx and fy. fx = (Simplify your answer.)

A:

Q: Evaluate the function g(x, y) at the point (4, –8). x2 + y2 g(4, –8) =

A: