Find and classify all critical points of f(x,y)%3Dx'+y-4xy+1.

Q: Compute the partial derivative of h(x, z) = ²xz-6x²z³. (Use symbolic notation and fractions where…

A: We have to partially differentiate the given function.

Q: Find the directional derivatives of the convex function f(x) = max{−5x + 3, 2x + 1}.

A:

Q: Let f (*= {(8) +f(9) for real values of x and y. If f '(0) exist 2 2 and equals –1 and f(0) = 1,…

A: Introduction :

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: 6 Y = x6 + Vx5 ++5 x3 y' = 6x5 +x² – 18x* y' = 6x5 +x1.5 – 18x-2 O Option 2 Option 1 y' = 6x5 +x15 –…

A:

Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices (- O),…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let F(x) = f(f(x)) and G(x) = (F(x)). You also know that f(8) = 6, f(6) = 3, f'(6) = 14, f'(8) = 3…

A: F(x) = f(f(x))F'(x) = dF(x)dx = df(f(x))dxF'(x) = f'(f(x))f'(x)F'(8)=f'(f(8))f'(8)        =…

Q: The total derivative of the function ƒ(x,y) =2x²y– xy is df = (2x² – x)dx +(4xy – y)dy b. df = (4x –…

A: df  = (df(x,y)/dx)dx + (df(x,y)/dy)dy f(x,y) = 2x^2y - xy df(x,y)/dx = 4xy - y df(x,y)/dy = 2x^2 - x

Q: Differentiate the function. ((5y + 1)3 Vy2 + 1 G(y) = In G'(y) =

A: Solve the following question

Q: determine the singular points of the given function, type of these points and calculate their…

A: The given function is                                      f(z)=1z2-4z+13

Q: y The function f(x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree 2x

A: Follow the procedure given below.

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(5) = 11, f(11) = 3, f'(11) = 6, f'(5) =…

A:

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: f(x, y) = ex + tan(x + y2).

A:

Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

A:

Q: In substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y…

A: In part (2), we have the following: ∂g∂x4,1,2=-π1 sin4π -14-1 ln3log332 Now, sin4π=0 So,…

Q: Is |3x-1| a function?

A: A relation is said to be a function only when every point in the domain has a unique value in the…

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

A: