Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = 6x² - 12xy + 2y³ - 18y: (-1,-1), (3,3) What is the nature of the function at (-1,-1)? OA. f(x,y) has neither a relative maximum nor a relative minimum at (-1,-1). O B. f(x,y) has a relative minimum at (-1,-1). OC. f(x,y) has a relative maximum at (-1,-1). OD. The second-derivative test is inconclusive at (-1,-1). What is the nature of the function at (3,3)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (3,3). OB. f(x,y) has a relative minimum at (3,3). OC. f(x,y) has a relative maximum at (3,3). OD. The second-derivative test is inconclusive at (3,3). ...

Q: true or false :  There exists a function F of two variables x, y such that dF = (x − y)dx + (x +…

A:

Q: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

A:

Q: ind the slope in the x-direction at the at P(0, 2, ƒ(0, 2)) on the graph of f when f(x, y) slope = 0…

A: We will find the required.

Q: (늘 가 G-2). Find the value. A relative extrema of the function f occurs at f(x, y) = 9x2 + 3y2 - 9x +…

A:

Q: Differentiate the function. c² – z² c2 + z? H(z) = In

A:

Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

A:

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

A:

Q: Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find a function f for x>0 so that f(x,y)=yf(x)+yf(x)

A:

Q: Let f(x) = x2. Give an equation of the line that intersects the graph of f(x) at x = 0 and x = V2.

A: Given data:     The given function is: f(x)=x2. The first value of x is: x1=0. The second value of x…

Q: How can you display the values of a function ƒ(x, y) of two in-dependent variables graphically? How…

A: For a  function ƒ(x, y) of two in-dependent variables. It can be plotted graphed using 3d plotting…

Q: When would you use a partial derivative? When you only need to differentiate half of a function. O…

A:

Q: Consider the following function which is defined for all x and y: ƒ(x, y) = 2(1 − p²)x²y² − x² - y²…

A:

Q: Determine whether the pairs of the functions are linearly inde- pendent or linearly dependent on the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: Find the partial derivatives of the function with respect to each variable.

A: