1a.Find the equation of the tangent plane to the surface √ x + √y + √...

1a.Find the equation of the tangent plane to the surface √ x + √y + √ z = 4 at P(1, 1, 4).

1b.Let f be a function of x and y such that fx = 3x − 5y and fy = 2y − 5x, which of the following is always TRUE?

a. (0, 0) is not a critical point of f.

b. f has a local minimum at (0, 0)

c. f has a local maximum at (0, 0)

d. (0, 0, f(0, 0)) is a saddle point of z = f(x, y).

e. None of these.

Solutions

Expert Solution

Finding partial derivatives of the given surface at the point P

Substituting these values in the tangent plane equation

Finding the critical point

Option (d) is TRUE since the critical point is the saddle point.

milcah answered 1 year ago

Next > < Previous

Related Solutions

Find the equation of the tangent plane to the surface x + y^2 + z^3 +...

Find the equation of the tangent plane to the surface x + y^2 + z^3 + sin(x − yz) = 7 at the point (2, 2, 1).

Find the equation of the tangent plane to the surface, (4x^2)(y^3) + (5yz) + (2xz^3) =...

Find the equation of the tangent plane to the surface, (4x^2)(y^3) + (5yz) + (2xz^3) = 7 at the point P(-1,1,1). Also nd the parametric equation of the normal line to that surface at that point . Sketch a picture that illustrates what this is all about.

12a Find an equation of the tangent plane to the surface ? = 2? 2 +...

12a Find an equation of the tangent plane to the surface ? = 2? 2 + ? 2 − 5?, ?? (1, 2, −4). 12b If ? = ? 2 − ?? + 3? 2 and (?, ?) changes from (3, −1) to (2.96, −0.95), compare ∆? and ??. Calculus 3 question. Please help.

Find the equation of the plane tangent to the function f(x, y) = (x^2)(y^2) cos(xy) at...

Find the equation of the plane tangent to the function f(x, y) = (x^2)(y^2) cos(xy) at x = y = π / √ 2 . Using this linearization to approximate f, how good is the approximation L(x, y) ≈ f(x, y) at x = y = π / √ 2 ? At x = y = 0? At (x, y) = (π, π)?

Find the vector equation of the tangent line to the surface f(x, y)=x/(1+y)+e^(x+y) at the point...

Find the vector equation of the tangent line to the surface f(x, y)=x/(1+y)+e^(x+y) at the point (-1,1,1/2) that is parallel to the xz-plane

Find an equation of the tangent plane to g(x,y)=e^(4x) -2xy+y^3 at (0,1)

2. (a) Find an equation of the tangent plane to the surface x4 +y4 +z4 =...

2. (a) Find an equation of the tangent plane to the surface x4 +y4 +z4 = 18 at (2, 1, 1). Find a derivative in direction (2,2,1) at point (2,1,1). (b) Use Lagrange multipliers to ﬁnd the minimum and maximum values of f(x,y,z) = 8x + y + z on the surface x4 + y4 + z4 = 18.

Question