Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point P in the direction of the given
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Calculus: Early Transcendentals (3rd Edition)
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- Compute the directional derivative in the direction of v at the given point. S(x, y) = xy – x, v=i-j, P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Duf(-1,2) = -22 Incorrectarrow_forwardCompute the directional derivative in the direction of v at the given point. S(x. y) = xy - x, v=i-j, P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(-1,2) =arrow_forwardCompute the directional derivative in the direction of v at the given point. f(x, y) = e*y-y, v = (12, –5), P = (-1,–1) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Duf(-1, –1) =arrow_forward
- Find the directional derivative of the function at the given point in the direction of the vector v. fx, y, z) = V xyz, (2, 2, 9), v = (-1, -2, 2) Pu(2, 2, 9) = Need Help? Read Itarrow_forwardCompute the directional derivative in the direction of v at the given point. f(x. y) = xy - x, v=i-j. P= (-1,2) Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(-1,2) = 22 Incorrectarrow_forward021 Bahar Which of the following is the directional derivative of f(x, y) =z²y at the point (-1,-1) in the direction of the vector i + 2j? O a. 0 O b. T V5 C. O d. Oe. hurava vaTınarrow_forward
- Find the directional derivative of f at P in the direction of a vector making the counterclockwise angle with the positive x-axis. 7 f(x, y) = 5√xy; P(1,4); 0= 3 NOTE: Enter the exact answer. Duf 1arrow_forwardFind the directional derivative of the function at the point Pin the direction the unit vector u = cos ôi + sin 0j. Sketch each the graph of the function, t point P, and the unit vector u. 2. f(x,y) = sin(2x + y), P(0, n), 0 = -.arrow_forwardFind the directional derivative of the function at the point Pin the direction of the unit vector u = cos ei + sin 0j. Sketch each the graph of the function, the point P, and the unit vector u. 3. f(x, y) = 3x – 4xy + 9y, P(1, 2), v = i +j.arrow_forward
- Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. 2.4 1.6 1. At the point (-1,1) in the direction of 0.8 of (-i +3)/v2, -0.8 v 2. At the point (0, –2) in the direction of -1.6 4.0 12.0 -2.4 (i – 2j)//5, -2.4 -1.6 -0.8 0.8 1.6 2.4 (Click graph to enlarge) ? 3. At the point (-2, 2) in the direction of i, 4. At the point (-1,1) in the direction of | (-i - 5)/v2, 5. At the point (0, 2) in the direction of j, 6. At the point (1,0) in the direction of - j, 12.0 10.0 12.0 10.0 10.0 8.0 10.0 12.0arrow_forwardUse the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. ? ✓1. At the point (1, 0) in the direction of -3. ✓ 2. At the point (0, -2) in the direction of (2-23)/√5, ✓3. At the point (0, 2) in the direction of 3, 4. At the point (-1, 1) in the direction of (-7+3)/√2, ? ? ? ? ? V 5. At the point (-1, 1) in the direction of (-7-3)/√2, ✓6. At the point (-2, 2) In the direction of 7, V > 2.4 1.6 0.8 0 0.8 -1.6- -2.4 12.0 12,0 10.0 10.0 -2.4 6.0 -1.6 -0.8 0 X 0.8 4.0 (Click graph to enlarge) 1.6 12.0 10.0 8.0 10.0 12.0 2.4arrow_forwardFind the directional derivative of the function at P in the direction of v. fx, y) 3 х3 - уз, Р(6, 3), v 3D (i + j) еВook Submit Answerarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage