Let f a function that allows second derivatives: Vf(x, y) = (a²x-a²x², y² + ay) With a <0, it can be stated certainly that: A) The point (1,0,f(1,0)) is a saddle point of f and f reaches a maximum relative in the point (0,0). B) The point (0,0,f(0,0)) is a saddle point of f and f reaches a minimum relative in the point (0,- a). C) f reaches a maximum relative at point (1,0) and f reaches a minimum relative at point (0,0). D) The point (0,a, f(0,a)) is a saddle point of f and f reaches a maximum relative in the point (1,0).

Q: If y is a differentiate function of x, then the slope of the curve of; xy^2-2y+4y^3=6 At what…

A: given that y is a differentiate function of x then we have to find the slope of the given curve at…

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: Let f(x, y) = x² + 5y². (a) Find f (5, 1) and f,(5, 1). fx(5, 1) fy(5, 1) =

A: Find

Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

A:

Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

A:

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: Determine the local min/max or saddle points of f(x, y) = x^2 + 2y^2 − 4x + 4y + 6 and make sure you…

A:

Q: Find the direction for which directional derivative of f (x,y) = 3x² – 4xy + 2y² +29 at (-2,3) is…

A: Formula: The maximum directional derivative of f(x, y) at (a, b) is given by ∇f(a, b) and direction…

Q: 6. (a) Let f(x, y) = x³y*. Find the directional derivative of f in the direction of T = (3, 4) at…

A:

Q: Q4A)If (3¹)(b)=(1314), find values of a, b, c, d . B)Find maximum and minimum directional derivative…

A:

Q: In the function f(x, y) = ((2x + 3y)^10), we need to know the derivative in relation to the variable…

A:

Q: Which of the following straight lines are tangent to the curve y = x³ + 4x2 + 7x and passes through…

A: Topic = Geometry  y=7x ia the tangent to the curve.

Q: Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).

A: