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A: Applications of derivatives
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- Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 1, 1) in the direction of the vector √5 (Use symbolic notation and fractions where needed.) directional derivative: + 2 √5Find the Directional derivative of the function f(x,y, z) = Vx² + y² + z² from point (1,2, –2) in the direction of vector v = (-6,6 ,–3). %3DFind the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction of the vector 1 2 i+ (Use symbolic notation and fractions where needed.) directional derivative:
- find the directional derivative of the function in the direction of the vector vFind the directional derivative of f(x,y,z) = z3-x2y at the point (4, -3, 4) in the direction of the vector v = <-1,-3,-2>.Find the directional derivative of the function: f(x, y) z² + 4y at the point (0, 0) in the direction of the vector (– 3, 1). You may enter your answer as an expression or as a decimal with at least 4 significant figures. |
- Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point (4, - 5) The unit vector that is normal to the level curve of the function f(x, y) isCalculate the directional derivative of g(x, y, z) = z² - xy + 4y2 in the direction v = (1,-4, 3) at the point P = (3, 1, -9). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(3, 1,-9) =Find the direction in which the maximum rate of change occurs for the function f(x, y) = 4x sin(xy) at the point (1,5). Give your answer as a unit vector. (sin(5) + 5 cos(5))i + cos(15) i 1+ (5 cos (5))² + 10 sin(5) - cos (5) x Invalid notation. syntax incomplete.
- Directional derivative of p = 2xz - y2, at the point (1, 3, 2), becomes maximum in the direction of 1. 4i + 2j – 3k 4i — бј + 2k 3. 2i – 6j + 2k 4. 4i - бј - 2k 2.Calculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt IncorrectFind the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = x²y + y²z, (2, 4, 6), v = (2, -1, 2) Duf(2, 4, 6)