1. See the document titled "Graded HW 2: Lagrange Example" in the Graded HW section. The...
4. (8 pts.) The level curves of z = = f (x, y) are given along with the constraint curve g(x, y)= 8 9(x, y) = 8 40 50 60 70 0 30 20 10 a. Maximize and minimize f on the constraint. b. Label the point where the maximum occurs as A and the point where the minimum occurs as B. c. Sketch in the approximate vectors Vf and Vg at the points A and B.
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
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...
Please help on my elementary calculus hw :) - Stephany 2. A commodity has a demand function modeled by p = 1700 -0.016x, and a total cost function modeled by C = 715,000 + 240x. (a) Find the profit and marginal profit at 2 = 700 units. (b) What price yields the maximum profit. (c) Use differentials to approximate the change in profit as the number of units sold changes from 500 units to 525 units. 3. Use implicit differentiation...
(1 point) Consider the function f(x) = x2 - 4x + 2 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval. on f(x) is on [0, 4); f(x) is (0, 4); and f(0) = f(4) = Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c and enter them as a comma-separated list. Values of се (1 point) Given f(x)...
f(x,y)=e^(2^y2-x^2+4y) 1.what is fxx fxy and fyy? 2. use the method of Lagrange multiplier to find local max and min of f(x,y)=x^2-y sbuject to constraint g(x,y)=x^2+y^2-1=0.
full workings required Let f: R^2 → be a differentiable function and let CCR be a curve in R^2 described by the cartesian equation f(x,y) = Letla.b) R be a point that lies on the curve Cck and assume that the partial derivatives off evaluated at (a,b) satisfy: fr(a,b) 0 and fy(a,b) +0. Also assume that there exists an expression y-g(x) that solves the equation f(xxx)=0 fory in terms of x in a neighbourhood of the point (8.b). This means...
6. (a) Newton's method for approximating a root of an equation f(x) 0 (see Section 3.8) can be adapted to approximating a solution of a system of equations f(x, y) 0 and gx, y) 0. The surfaces z f(x, y) and z g(x, y) intersect in a curve that intersects the xy-plane at the point (r, s), which is the solution of the system. If an initial approxi- mation (xi, yı) is close to this point, then the tangent planes...
Please answer clearly and step by step, thank you!!!! 1. Below is a function f for which f' and t” have already been computed for you. f(x) = 24 – 43% + 162 ' (t) = 4(x + 1)(x - 2) 2 f "(t) = 122(x – 2) (a) Find the intervals where f is increasing/decreasing (or write "none"). Also find the L-values where a local maximum/minimum occurs (or write "none.") Increasing on: Decreasing on: Local Max(s) at 2= Local...