Find the second partial derivative fry of z = f(x, y) = 12x³y - 8x. A) 36x2 - 8 B) 36x2y4 Write the answer as a letter A,B,C, or D. C) 144x²y Question 22 (4 points) Find extremum of value of f(x, y) = 3xy subject to 2x + 3y = 24 minimum of 48 at (6,6) D) 144x²y³

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

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

A:

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

A:

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

A:

Q: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

A:

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

A:

Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

A:

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

A:

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

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

A:

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. 6. V12…

A:

Q: Prob3: Find the derivative of the function at P, in the direction of A f(x,y,z) = (1.0.). = cos xy +…

A:

Q: Which is the greater rate,15 miles in 12 minutes or 25 miles in 20 minutes?Explain

A: Solution: the objective is to find sum of given series

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

A:

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3…

A: Given y5=kx5 To find the orthogonal trajectory

Q: //welro) Find a local linear approximation for the function 5х + 6 f(x) valid for x near 5 5x + 6…

A:

Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

A:

Q: Form the partial cquatins by eliminating the fiam differential z- Qta) (?+b) atbiliary constant)

A: We have to form the partial differential equations by eliminating the arbitrary constants from…

Q: Find the indicated value for f(x,y) = x^2y^3  fxx(1,2) =  fyy(1,2) =  fxy(1,2) =  really…

A: Given query is to find indicated partial derivative.

Q: 3 x° In x x° with respect to X - Find the derivative of y a) 6x - a2 b) None of these c) p6 ln x x2…

A: Given query is to find the derivative of the expression.

Q: 1. Let f(x) = x³ – 5x + 2, Use Derivative Rules to find the following: a) Find the equation of the…

A:

Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

A: