f(x, y) = 5eª cos y, (a,b) = (0, 7), a. Calculate the directional derivative of f at the point (a, b) in the direction defined by 7. & P b. Find the direction at (a, b) in which the rate of change of f is greatest. and v = (5,3). c. Find the maximum rate of change. 团 d. Fill in the blank: f decreases the most at (a, b) in the direction of

Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. 2.4 ? 1. At the point (0, 2) in the direction of j, 1.6 ? 2. At the point (-1, 1) in the direction of (-i – j)/V2, 0.8 ? 3. At the point (-2, 2) in the direction of i, -0.8 ? 4. At the point (0, –2) in the direction of (i – 2j)/V5, 1.6 4.0 ? 5. At the point (1,0) in the direction of -j, -2.4 ? 6. At the point (-1, 1) in the direction of (-i + j)/v2, -2.4 -1.6 -0.8 0.8 1.6 2.4 (Click graph to enlarge) 12.0 10.0 12.0 10.0 10.0 12.0 8.0 10.0 12.0

Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero. 2.4 Negative 1. At the point (-2,2) in the direction of i, 1.6 Positive 2. At the point (0, 2) in the direction of j, 0.8 Positive 3. At the point (0, –2) in the direction of (i – 2j)/V5, ? 4. At the point (-1, 1) in the direction of (-i + j)//2, 0.8 -1.6 ? v 5. At the point (1, 0) in the direction of –i, 4.0 -2.4 Zero 6. At the point (-1, 1) in the direction of (-i – )/V2, 2.4 -1.6 -0.8 0.8 1.6 2.4 (Click graph to enlarge) 12.0 10.0 12.0 10.0 O'g 10.0 12.0 10.0 12.0

Use 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 2.4