9. Let F be the same as in the previous problem, but this time let P be the line segment from (5,0, 3) to (1, 1, 1). Find pF. dr.

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A:

Q: Find fx, fy, fz. fx = + +2² f(x,y,z) = e¯ (4x²+2y² 12=7 Z

A: f(x,y,z)=e-(4x2+2y2+z2)we know (i)  ∂ ∂x(xn)=nxn-1(ii)  ∂ ∂x(constant)=0

Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: f(x,y) = x² + 3y² + +xy b. f(x,y) = /x² + y² a. %3D

A:

Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +…

A:

Q: f(x, y) = √√2x² + 5y² fz(0, 1) =

A:

Q: Consider the function - f(x, y) = 2x² + xy² − 6xy + 5x +2. (a) Show that (1,3) is a stationary point…

A:

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

A:

Q: Given f(x, y) = 2x² + 6xy² + y³, find frz(x, y) = fry(x, y) =

A:

Q: Solve Fyy + 3 Fxy + 2 Fxx = 2x, F(x, 0) = -x, 2, F(x, 0) = 0. F(x, y) =

A: General solution is given by complementary factor + particular integral.

Q: fo Find mini

A: Given :   fx, y=x+y+27xy

Q: 30. Which of the following is the value of f.(2, -1)? O -13 O 50 O 106

A: Given :              f(x, y) = 2x3 + 7x2y3 + 8y3 + 3x - 2y + 10   To find the value of fx(2,…

Q: 3 – 1 х — 6 f(x) = - Where are the critical numbers? (Separate multiple answers with commas.) X =

A:

Q: f(x, y) = V 2 2 3x² + 4y²

A:

Q: x² + y² – 4 hat fa(x, y) = 2 Va² + y? · V9 - (Vx² + y? – 4) r2 |

A:

Q: Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A: The given function .The aim is to find all values of  and  such that .

Q: For f(x, y, z) = x² - y² + z², find f(2, -1, 4).

A:

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: If f(x,y)=2y2ex+3ln(xy), find fxyy(1,1).

A: Given  fx,y = 2y2ex + 3lnxy                        fxx,y = ∂f∂x = 2y2 ∂∂xex + 3∂∂xlnxy…

Q: f(x, y) =  5 xy +  xy 8; find fx, fy, and fyy

A: Partial derivatives

Q: -

A: Given function is: fx,y=2x3+7x2y3+8y3+3x-2y+10 We have to find fxx,y.

Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

A:

Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

A:

Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32