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- How are the absolute maximum and minimum similar to and different from the local extrema?Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematics9. A rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given that the available materials for the fence are good for 24m, what dimensions will produce a maximum area for the fence? What is the equation that will give us the function's critical point/s
- Find the critical points and test for Maxima/Minima. Show your complete solution.On the interval 2 < x < 4, there is a relative… •maximum •minimum •increasing •decreasing •constantDoes ƒ(x) = 2ex/(1 + x2) have an absolute minimum value? An absolute maximum? If so, find them or give reasons why they fail to exist. List all critical points of ƒ.
- On the interval -2 < x < 1, the function is… •maximum •minimum •increasing •decreasing •constantA closed right circular cylinder will be built with two types of metal. The base and the top of the cylinder will be constructed of metal that has a value of $ 2 per cm2, while The side surface of the cylinder will be constructed of a metal that costs $ 2.5 per cm2. The function that allows to minimize the cost of manufacturing said cylinder is given by: the answers are in the first attached image2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints: y = 2x2 + 4x + 5, [0, 2]Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or minimum at the critical point?