Question

Suppose f(x,y) = x/y , P = (-3, -3) and v = 1i - 4j. 1. Find the gradient of f. ?f(x, y) = 1/y i + -x/y^2 j 2. Find the gradient of f at the point P. ?f(P) = -1/3 i + 1/3 j 3. Find the directional derivative of f at P in the direction of v. Du f(P) = 9/3 4. Find the maximum rate of change of f at P. ?18 5. Find the (unit) direction vector in which the maximum rate of change occurs at P. i + j

          Suppose f(x,y) = x/y , P = (-3, -3) and v = 1i - 4j.
1. Find the gradient of f.
?f(x, y) = 1/y i + -x/y^2 j
2. Find the gradient of f at the point P.
?f(P) = -1/3 i + 1/3 j
3. Find the directional derivative of f at P in the direction of v.
Du f(P) = 9/3
4. Find the maximum rate of change of f at P.
?18
5. Find the (unit) direction vector in which the maximum rate of change occurs at P.
i + j

Suppose f(x,y) = x/y , P = (-3, -3) and v = 1i - 4j.
1. Find the gradient of f.
?f(x, y) = 1/y i + -x/y^2 j
2. Find the gradient of f at the point P.
?f(P) = -1/3 i + 1/3 j
3. Find the directional derivative of f at P in the direction of v.
Du f(P) = 9/3
4. Find the maximum rate of change of f at P.
?18
5. Find the (unit) direction vector in which the maximum rate of change occurs at P.
i + j

Added by Ashlee H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Steven Clarke

Step 1

To find the gradient of f, we need to find the partial derivatives with respect to x and y. Since we don't have the function f(x, y), we cannot find the gradient ∇f(x, y). Show more…

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Suppose f(x, y) = x/y, P = (-3, -3) and v = 1i - 4j 1. Find the gradient of f ∇f(x, y) = 1/y i + -x/y^2 j 2. Find the gradient of f at the point P ∇f(P) = -1/3 i + 1/3 j 3. Find the directional derivative of f at P in the direction of v Du f(P) = 9/3 4. Find the maximum rate of change of f at P √18 5. Find the (unit) direction vector in which the maximum rate of change occurs at P i + j