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- maximize f(x,y)=xy subject to the contraint 6x+y=18 the last question is what is the maximum valye of xy?Find the linearization of the square root function, f(x)=√xf(x)=x at x=4L(x) = Estimate squareroot of 3 Estimate squareoot of 6An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting outx-inch by x-inch squares from the four corners and bending up the sides. The largestpossible volume of the box is obtained by maximizing V (x) =_________ for x in the interval _________
- An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by x-inch squares from the four corners and bending up the sides. The largest possible volume of the box is obtained by maximizing V (x) = _______ for x in the interval____. .How did you apply the concept of maxima/minima in answering the problem? Angelo, who is in a rowboat 2 kilometers from a straight shoreline wishes to go back to his house, which is on the shoreline and 6 kilometers from the point on the shoreline nearest Angelo. If he can row at 6 kph and run at 10 kph, how should he proceed to get to his house in the least amount of time?Find the critical points for the function: f(x,y)=40+x3(x-4)+3(y-5)2 Are these points local maxima, local minima, or saddle points?
- Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?Find all the local maxima, local minima and saddle points of the function f(x,y)=3+2x+2y-2x2-2xy-y2Consider the following. y = 2x3 − 12x2 + 6 (a) Find the critical values of x of the function. (b) determine the relative maxima and minima. (If an answer does not exist, enter DNE.)
- Q1 : a) For the function f(x )=x^3 −12x,its local maximum is ____?____ which occurs at (___? __ ;its local minimum is ____?____ which occurs at (___? __ ;According to Poiseuille's law, the speed S of blood through an artery of radius r at a distance x from the artery wall is given by S = k[r^2 - (r- x)^2] where k is a constant. Find the distance x that maximizes the speedLet p= 23 - square root x and C(x)= 254 +3x, where x is the number of garden hoses that can be sold at a price of $p per unit and C(x) is the total cost (in dollars) of producing x garden hoses. (A) Express the revenue function in terms of x. (B) Graph the cost function and the revenue function in the same viewing window for 0≤x≤529. Use approximation techniques to find the break-even points.
