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
17.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Calculus: Early Transcendentals, 2nd Edition
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- determine directional derivative of the functionarrow_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_forwardI would need help with a, b, and c as mention below. (a) Find the gradient of f.(b) Evaluate the gradient at the point P.(c) Find the rate of change of f at P in the direction of the vector u.arrow_forward
- Determine if the derivative of the vector-valued function exists at the specified point. (Your instructors prefer angle bracket notation for vectors. If the derivative exists at the specified point, enter its value. If the derivative does not exist, enter DNE.) FC) = (coste), tan(t), 3t cos(t) at t, =arrow_forwardUse 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 12.0arrow_forwardq13arrow_forward
- Determine the domain of the vector function r(t) = cos(4t) i + 7In(t - 5) j - 10 k Evaluate if the vector function is possible at the value of t=8, round to two tenths Find the derivative of the vector function r(t)arrow_forwardF question 13arrow_forwardUse 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 12.0arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning