4. For some curve y = f(x), consider the function (x) which gives the angle between...
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...
a) Consider the function y=x(3-X). A function of this form will have which of the following? Hint: Determine the functional dependence of your function (linear, quadratic, cubic etc.) and relate your findings to Q3 of pre-lab 2A. O A global maximum O A global minimum Neither a global maximum nor a global minimum b) At what x-position, if any, will the global maximum or minimum of the function occur? Enter O if no such point exists. c) If we instead...
Consider the following graph of f(x) on the closed interval (0,5): 5 4 3 2 1 0 -1 0 1 2 3 5 6 (If the picture doesn't load, click here 95graph2) Use the graph of f(x) to answer the following: (a) On what interval(s) is f(x) increasing? (b) On what interval(s) is f(x) decreasing? (c) On what interval(s) is f(x) concave up? (d) On what interval(s) is f(x) concave down? (e) Where are the inflection points (both x and...
| Sketch the curve of the function f(x) = + unction f(x) = "* [r'(x) = 2*, S"(x) = 205*] Do this by determining the following information: domain, vertical asymptotes and limit - behavior, horizontal asymptotes, x \& y intercepts, symmetry, intervals of increase/decrease and maximum/minimum points, intervals of concavity and inflection points
3. Suppose f(x,y,2)-sin2(x)-2sin(x) + y. 4 y z + 52.62. Find the minimum value of this function. you must find the point at which the minimum occurs and "prove" that the function really has a mini mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should...
(1 point) The figure below gives F'(x) for some function F 4 5 Use this graph and the facts that the area labeled A is 9, that labeled B is 8, that labeled C is 2, and thatF(2) = 5 to sketch the graph of F(x). Label the values of at least four points. Then, using your graph, give four (x, y) points on the curve (Give your answer as a list of points separated by commas.) (1 point) The...
Homework 4: Problem 3 Previous Problem Problem List Next Problem (6 points) Consider the function f(x, y) - (e - x) sin(y). Suppose S is the surface z- f(x, y) (a) Find a vector which is perpendicular to the level curve of f through the point (5,5) in the direction irn which f decreases most rapidly. vector (b) Suppose u = 31 + 3/4 ak is a vector in 3-space which is tangent to the surface S at the point...
Recall: For a function y = f(x), the critical points are (c,f(c)) for all c for which f,(c) = 0 Each such point is a relative maximum if f"(c) < 0 and a relative minimum if f"(c) > 0 For the following functions, find all critical points and determine if they are relative minimum or maximum, if possible. y-x2-4x 1 y=x3-6x2 + 9x-2 (4 У х Recall: For a function y-(x), the inflection points are (d.f(d)) for all c for...
Consider the function f(x,y)=(ex-2x)sin(y). Suppose S is the surfacez=f(x,y).(a) Find a vector which is perpendicular to the level curve of through the point (4,6) in the direction in which f decreases most rapidly.vector =(b) Suppose v=5i+7j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,6). What is a?
33) At the point shown on the function above, which of the following is true? f'<0,f''<0 f'<0,f''>0 f'>0,f''<0 f'>0,f''>0 34) The function graphed above is decreasing on the interval ____ < x < ____ The inflection point is at x = ____ 36) Consider the function f(x) = 1−5x2, −5 ≤ x ≤ 2. The absolute maximum value is and this occurs at x = _____ The absolute minimum value is and this occurs at x = ______ & t &...