*4:Which of the following functions has gradient vector [4x₁x₂ 2x² 3x3]¹?A: f(x) = 2x³ + 2x3 + x²x²B:f(x) = 2x²x₂ + x³C: f(x) = 2x²x₁ + x²D:Non of theseABC

To find: Which of the given functions has the gradient ∇f=4x1x2 , 2x12, 3x32T.

Answered: 4: Which of the following functions has…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

See similar textbooks

Similar questions

Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].
Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by W(f1,f2)=e2xW(f1,f2)=e2x. Are the functions that you found linearly independent on (−∞,∞)(−∞,∞)? How do you know?
Compute the gradient of f(x,y) = 9-5x^2-y^2 and evaluate it at the point (4,-1)
What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?
Determine the orthogonal trajectories of the family of electric field lines described by the family (x-c)3 + y2 - c2 (3x-c) = x3
Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to:
Find the linearization L(x) at x=a.
What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?
Determine two functions, defined on the interval ( − ∞ , ∞ ) , whose Wronskian is given by W ( f 1 , f 2 ) = e 2 x . Are the functions that you found linearly independent on ( − ∞ , ∞ ) ? How do you know?
Let f be a function defined in R2 by f(x,y) = 3x2 - 2x3 - 3y2 + 6xy. Find the gradient vector in point P(0,1)

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

4: Which of the following functions has gradient vector [4x₁x₂2 2x² 3x3]¹? A: f(x) = 2x³ + 2x³ + x²x² B: f(x) = 2x²x₂ + x³ C: f(x) = 2x²x₁ + x² D: Non of these A B О с O D