(1 point) A contour diagram for a function f(x,y) is shown below. 4 --- - --...
Answer the following questions for the given contour diagram of
f(x, y) below:
a. Estimate ∇f(4, 1)
b. Estimate the maximum and minimum rates of change of f at the
point (4, 1)
c. In two different ways, estimate the rate of change of f at
the point (4, 1) in the direction of the vector < −1, 1 >
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2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
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...
1) The contour map of 2 =/(x,y) is shown below. Use a Riemann sum to approximate the integral S(x,y) dx dy and then use that same Riemann sum to estimate the average value of f(x,y) over the region R = (0,4] [0,2]. K-12 ko -62 k>4 6 K 2
(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...
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)
17 marks] Consider the functionf(x, y) = (y - 1) (x- 1). (a) Find a unit normal vector to the contour line given by f=0.5 at the point (x,y) (1.5,2). Do not forget to check that this point is on the contour line. (b) Consider the curve L given by r(t) = 2ti+3tj with 0 ts1 and the Cartesian basis vectors i= (1,0) and j= (0,1) of R2. Determine using the chain rule and use this result to determine all...
(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...
Question 20 Classify the point (1, 1) by the function f(x, y) = 4 + x3 + y2 – 3xy. Not a critical point Absolute minimum Local maximum Local minimum Absolute maximum None of the above or below
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...