5) The level curves of a function f(x,y) are given in the graph below. 2 X...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P rty. I 5. [16...
5. Consider the function f: R -> R given by f (x, y) := e°+v* _ 4. (a) Sketch the level curves of f. (5 marks) (b) Find Vf, the gradient of f, and determine at which points Vf is zero. Remark: These points are called the critical points of f (5 marks) (c) Determine whether the critical points of f are local minima, local maxima, or saddle points by considering the level curves of f. (5 marks) (d) Calculate...
5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c) Sketch Vf at P and Q on the level curve f(x, y) = 3. 5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c)...
e ana the gradient IV.1 The level curves of the function z fix, y) are sketched in the figure below: 20 50 100 10 150 10 20 30 Let u= (l,-) and v=죠(1,1) Estimate the derivatives at the indicated point: DJい IV.2 (The Directional Derivative) Compute the derivative of the function f(x,y,z)-sin(2x-y)+ cos(2y-2) Ft%r,-r) in the direction of the vector". (-2,-1, 2) at the point e ana the gradient IV.1 The level curves of the function z fix, y) are...
2. (20pt.) Let f(x, y) 2 (a) draw and describe the level curves of f of value c= 0,1,2,4 (b) sketch the graph of f (r.y) 2. (20pt.) Let f(x, y) 2 (a) draw and describe the level curves of f of value c= 0,1,2,4 (b) sketch the graph of f (r.y)
. Given that the domain off(xis-2 i Let f ( ) be function ) and range is-10 x a 6 . that the point (3, f(x): is on the graph of f(x), answer the following questions for the various transformations of (a) For the transformation fx-1) i. describe how its graph relates to the graph of f(x). ii. find the domain. ii. find the range. iv. find a point that must be on the graph. v. Did the order of...
7) Let D be the domain described by -1 <y<1, x 2-1, r< y2 i) Sketch the domain D. neither? Is D horizontally simple, vertically simple, ii) Calculate the three integrals a = ffpxdxdy, b = SSpydxdy and iv) What physical meaning does the quantity What physical meaning does the point (a/c, b/c) have, related to the region D? or SSp drdy have, related to the region D? i) C= v) 5) The level curves of a function f(r,y) are...
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map of the function f(z, y)2s y 1 that contains four level curves. Make sure to find an equation for each level curve and label each one on the graph. IQuestion 3] The equation of the tangeat plane to the function z the equation: Using the form of the equatioa above, fiud the tangent plane to f(a,y)yat the point (2. ). Question 4] Find...
The graph of y = f'(x), the derivative of a function f. 600,00) is given below: y= f'() Which of the following must be true? of is decreasing on (2, 4) and concave down on (-3,3). of is increasing on (-2, 2) and concave down on (0,4). f is increasing on (-3,0) and concave down on (0,4). fis decreasing on (0,4) and concave down on (-2,2).
7 Olet f(x,y)= -(--) Cy-x)+2 a) sketch flx,y) b) Draw the level curves f(x, y) = for t=2, 10, 1-2 08 c) Compute f (33) what point represents this computations, what are the signs (²) of fx (3,3), ty (3,3), +*x (3,3), toy (3,3)? point part b) ? a d) Without and