Please help. 16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59 16, Figur...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
(1 point) Determine the sign of fe and fy at each indicated point using the contour diagram of shown below. (The point P is that in the first quadrant, at a positive z and y value; Q through T are located clockwise from P, so that Q is at a positive r value and negative y. etc.) 6 2 P 8 (a) At point Q f is? and fy is (b) At point R is and fy is (c) At...
41. (а) Let f(х, у) 2 + y2. Estimate fr(2,1) and fy(2, 1) using the contour diagram for f in Fig- ure 14.21 (b) Estimate fa (2, 1) and fy(2,1) from a table of values for f with (c) Compare your estimates in parts (a) and (b) with the exact values of fa (2,1) and fy(2,1) found al gebraically. 0.9, 1,1.1 1.9, 2, 2.1 andy y 3 2 1 -3 -1 2 3 -3 -2 1 Figure 14.21 T 41....
The contour diagram in Figure 6(a) describes the hyperbolic paraboloid z = f(x, y) = I y. The bold lines represent the r and y axes. (a) (b) Figure 6 i) Through a change of variables u = r+y and v = r-y, show that f can be rewrit- ten in the standard form of a hyperbolic paraboloid. Such a transformation is shown in Figure 6(b) where the bold lines now represent the u and v axes. az ii) Use...
Multivariable Calculus Question 3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe 0.8 0.8 1.6 2.4 24 1.60.80.8 16 24 2.4 3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe...
Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide ir the speciñied directional derivatives below are positive, negative, or approxmately zero 14 (a) At point (-2,2). in direction-i. is.? (b) At point (0,-2) in direction- i f s ? (c) At point ( 1,1), in direction i + s ? a) At point (-1,1), in direction +j f: s ? (e) At point (0,-2), in direction it2j. fd is!? n At point (0,-2),...
I'm having trouble with b and e 46. Use the portion of the contour diagram of f(x,) shown below to estimate the following: 80 78 76 74 72 113 6 9 12 15 18 21 24 (b) f (15,76) in the direction -i+j (d) vf di where C is the path from (15,76) to (24,76) (a) gradf (15, 78) (c) A critical point of f(x, y). (e) f(x,y)dA where R is the rectangle 9Sxs 15, 76 3 y s 80...
(1 point) Estimate f(-3.01,-1.97) given that f(-3,-2) = 5, fx(-3,-2) = -2 and fy(-3, -2) = 3. f(-3.01,-1.97) ~ (1 point) Find the linearization of the function z = x,y at the point (-5, 49). L(x, y) = (1 point) Find the equation of the tangent plane to z = ex + y + y4 + 6 at the point (0,3,91). z =
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative off in the direction v at the point P. (a) At the point P = (2, 2) in the direction ✓ = 7, the directional derivative is approximately O‘ot 16.0 18.0 12.0 14.0 2.0 (b) At the point P = (3, 2) in the direction ✓ = -1, the directional derivative is approximately 8.0 (c) At the point P = (4,1) in the direction...
1. (25 points) The figure below shows the contour plot of f(x,y)-3 -1 - 2y+y. (Credit for the figure is due to UMich instructors.) 6.00U 6.000 1.5 1.0 0.5 0.0 0.5 1.0 1.5 6.000 2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 (a) Find all critical points of f. There should be six. Mark them on the contour plot. (Think, but don't write, about how to guess the critical points from the contour plot.) (b) Find f-,) v(,),and fp()-fy(, y) (c) Try to...