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- Suppose that ∇fp =〈2, −4, 4〉. Is f increasing or decreasing at P in the direction v =〈2, 1, 3〉?Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.Suppose that the temperature in degrees Celsius at a point(x, y) on a flat metal plate is T (x, y) = 10 − 8x2 − 2y2,where x and y are in meters. Find the average temperatureof the rectangular portion of the plate for which 0 ≤ x ≤ 1and 0 ≤ y ≤ 2.
- Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.If f(20) = 68 and f′(20) = −0.025, local linear approximation predicts that f(18) will beequal toSuppose that f (4, 4) = 3 and fx (4, 4) = fy (4, 4) = −1. Use thelinear approximation to estimate f (4.1, 4) and f (3.88, 4.03).
- Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the point (1, 2)? How do you know?Eliminate the arbitrary constants in theequation. r is a parameter that must not beeliminated.Find the linear approximation of the f(x,y)= (x/x+y) at the point (1,4). Answer: f(x,y)=?