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- FInd the absolute extrema (maximum and minimum of the function on the region bounded by the square with vertices at (0,0),(7,0),(0,7), and (7,7)Locate the (a) relative minimum (x,y)=_____ and (b) the relative maximum (x,y)=_____The area of the region is bounded by the x-axis, the curve y = 6x – x2, the line x – 1 = 0 and the line x = 4. 3. Find the ordinate of the vertex of the curve y = 6x – x2. Find the area of the region. Find the distance of the centroid of the area from the y-axis.
- Find the local minimum, maximum, and saddle points – if any – of the function f(x, y) = 2x^2 + y^2 + 2x^2 y. Find the maximum and minimum values of the function f(x, y) = xy on the closed and bounded region defined as {(x, y) | x^2 + y^2 ≤ 1}. [Hint: You need to analyze the function first on the open region {(x, y) | x^2 + y^2 < 1} and then on the boundary {(x, y) | x^2 + y^2 = 1}.]find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = 4xy - x4 - y4 + 16 R: The triangular region bounded below by the line y = -2, above by the line y = x, and on the right by the line x = 2.Find the absolute maximum and ansolute minimum values of the function f(x,y)=6-x^2-4y^2 on the region R={(x,y)|-2 < or = x < or =2, -1 < or = y < or =1 }, as well as the points in the domian (x,y) where they occur. Please show all work and steps for me to follow. Thanks!
- Consider the function f(a,b) = a+b-a^2-b^2-ab over a closed interval with the endpoints (0,0), (2,0), (2,2), and (0,2). Locate the critical point inside of this square and find the absolute max and min of f, and the points they happen at all 4 boundaries. Based on the calculations what's the absolute maximum and minimum of this region ? Please show all steps and explain throughly.Find the absolute maximum and minimum values, and the points at which they are achieved, of the function f(x, y) = 2x2− 2x + y2 − y on the region given by 0 ≤ x ≤ 2, 0 ≤ y ≤ 1. Clearly identify all points at which an extreme value could possibly occur.Let y=X^x, X>0. Find the x where the function has a minimum value What is this minimum value?
- the continuous function has a critical point. (a)Is the critical point a local maximum or a local minimum? (b)Sketch the graph near the critical point. Label the coordinates of the critical point. 1. f(1) = 5, f ′(1) = 0, f ″(1) = −2 2. h(2) = −5, h′(2) = 0, h″(2) = −4A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture. Turbulence makes it difficult to directly measure the thickness of the slick at the source where x=0, but for x >0, it is found that y=0.5(x^2 + 3x)/x^3 + x^2 + 4x. Assuming the oil slick is continuously distributed how thick would you expect it to be the source?A raptured pipe in a North Sea oil rig produces a circlar oil slick that is y meters thick at a distance x meters from the rapture. Turbulance makes it difficult to directly measure the the thickness of the slick at the source (where x=0), but for x >0, it is found that y= 0.5(x2+3x)/x3+x2+4x. Assuming the oil slick is continiously distributed, how thick would you expect it to be at the source?