The maximum directional derivative of a function is given by the magnitude of the gradient vector. Then the maximum directional derivative of the function f(x,y) = x Iny + x²y² at point (-1, 1) is given by A. -21 +j B. 15(-21 + j) C. 1 D. 5 E. 15
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A: Formula Gradient of function f(x,y) ∇f(x,y) = fx(x,y)i + fy(x,y)j Where fx is partial derivative…
Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (8, 0) Vg(8, 0) =
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Q: 2x+1 The gradient vector to f (x, y) at the point (0, 0) y+1 is .
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Q: EXAMPLE 4 Find the directional derivative of the function f(x, y) = x²y³ - 5y at the point (2, –1)…
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Q: , Suppose f (x, y) = 4, P = (3,2) and v = 3i – 2j. - A. Find the gradient of f. (Vf)(x, y) : i+ j…
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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (9,…
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- Find the gradient of the function at the given point. z = x2y, (9, 1) ∇z(9, 1) = Find the maximum value of the directional derivative at the given point.8. Find the directional derivative of f (x, y, z) = xy z at P(2,1, 1) in the direction of Q(0,-3, 5)Find the gradient of the function at the given point. Function Point f(x, y) = x + 4y y + 1 (3, 3) ∇f(3, 3) = Find the maximum value of the directional derivative at the given point.
- Suppose that g is a function of two independent variables that has continuous partial derivatives, and consider the points P(8,6), Q(7,6), R(8,18) and S(6,7). The directional derivative of g at P in the direction of the vector PQ→ is 4, whilst the directional derivative of g at P in the direction of PR→ is 4. Find the directional derivative of g at P in the direction of the vector PS→. Give your answer correct to 2 decimal places. DPS→g(P)=let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the directional derivative at the point P0(-1,3,1) in the direction of the line parallel to 0x axis 21.We want to estimate f(1.01 , 0.97) for the function f(x,y)= √(4 - x2 - y2). For this, we can use an appropriate linearization of the function f(x,y).Then Fx (1,1) = ? and Fy (1,1) = ? therefore we can estimate the mentioned value obtaining an answer of f( 1.01 , 0.97) ≈ L( 1.01, 0.97) =
- The temperature of a solid is given by the function B(x, y,2) =x*y: +4x, where x, y, z are space coordinates with respect to the centre of the solid. Find the directional derivative of at P(1.-2.1) along a =2i-2j+k. What are the magnitude and direction of the fastest decrease of the temperature from the point P? Also find the divergence of the temperature gradient at P.(1 point) If the gradient of ff is ∇f=2z(i) +x (j) +yx (k) and the point P=(−8,−8,−2) lies on the level surface f(x,y,z)=0 find an equation for the tangent plane to the surface at the point PFind the gradient of pthe function and the maximum value of the directional derivative at the point (1;2)for g(x;y)=ln sqrt3 x^2+y^2
- 1) Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = <3, 1> from the point P = (5, 2).Demonstrate the use of the method with reflections on the use of numerical methods, find the minimum for the function below: F(x,y)= Ax^2 - Bxy- cy^2= x -y (Xo=4, Yo=4) A=2 B=-2 C=1 Identify the minimum again using the Newton’s method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step , solve first the and optimal using the condition . When taking the derivative of , please remember to consider the inner derivatives for each of the coordinate axes that results as dot product with the main function. In this work it is enough that only the second term in the dot product is analyzed using numerical derivatives. Thus, the function takes the form .Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0) and (1,2) with positive orientation. (b) Compute the directional derivative of the function f(x, y, z) = xy2 + y2z3 + z3x at the point P(4, -2, -1) in the direction of Q(l, 3, 2)