ask 4. Let F(z,y) = [2ry² + 1, 2r²y + y]. i) At the point (3,3) in which direction is the directional derivative of f maximal? What is the value of the direc- tional derivative of ƒ in this direction at (3,3)? ii) Find the equation of the tangent plane to z = In(2r + y) at (-1,3).

Q: Determine the directional derivative of f(x, y) = 3x² + [y] at the point P(-1, -1) along the…

A: Explanation of the answer is as follows

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: The temperature at the point (x, y) on a metal plate is X x² + y² Find the direction of greatest…

A: Given function:-T=xx2+y2

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: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Find the derivative of the function at P, in the direction of A. f(x,y) — - Зху + 4y*, Po(-6, - 5),…

A:

Q: Assume that w = f(s3 + t?) and f'(x) = ex. Find dw dw and at ds dw at dw

A:

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: What is the gradient of the tangent line to the curve y = 2x³ – 3x2 at the point with a = 2? |…

A:

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: At the point (1, −1), the function (x, y) has a derivative of 5 in the direction toward (3, 1) and a…

A: Consider the given information.

Q: the contour diagram of o decide if the specified directional derivative is positive, negative,…

A:

Q: Given: /(x, y) = 3x² – 2y² at (-÷.0) in the direction from P (–.0) to Q(0,1). What is the…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: value of the dir function

A: