Question 4 Your answer is CORRECT. Suppose that f is a differentiable function of x and y such that Vf(0, 0) = Vfƒ(1, 1) = 0. Given that fax (x, y) = -12x + 4y +3, fay(x, y) = 4x - 2y, and fyy (x, y) = -2x - 6y-3 which of the following is true? a) b) c) d) e) f(0, 0) is a local minimum and f(1, 1) is a local maximum. (0, 0) is a saddle point and f(1, 1) is a local maximum. (0, 0) is a saddle point and f(1, 1) is a local minimum. Both (0, 0) and (1, 1) are saddle points. f(0, 0) is a local maximum and f(1, 1) is a local minimum.

Q: Find and classify all stationary points of the function f(x,y) = x³ + xy + y² − x.

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

A:

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r - s, s² - 7r). Use the table…

A: ​gr​(7,6)=−50gs​(7,6)=93​Explanation:Step 1:​Given a Table of values of f,g and fx​,fy​​​To find:…

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: . Sketch the level curves of the function f(x, y) = x² + 2x + y² – 6y corresponding to the z-values…

A:

Q: Sketch the level curves of the function corresponding to each value of z. f(x, y) = 9x² + y; z = -2,…

A:

Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)

Q: Suppose that f(-1) = 2 and f(1) = 2 for a differentiable function on [–1, 1]. Compute the slope of…

A: Given: The function is differentiable in -1,1. Also, f-1=2 and f1=2 Since, slope of the line, m…

Q: Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3,-4, -3) in the direction…

A: