Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine whether each corresponds to a local minimum or maximum. Let f(x) = x exp(-x²) Critical Point 1 = is what by the Second Derivative Test ? Critical Point 2 = is what by the Second Derivative Test v ? No "oblem. Local Max ers Local Min Yc Yc Test Fails
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- Analyze the functions whose derivatives is given below. What are the critical points of ƒ? On what open intervals is ƒ increasing or decreasing? At what points, if any, does ƒ assume local maximum and minimum values?3. Determine the critical points for the function below and use the second derivative test to decide if the point is a local maximum or a local minimum.Find all critical point(s) of f and use the Second Derivative Test to determine whetherf has saddle point or a relative maximum or minimum at each of those points. Pls. show complete solution and right answer. Thanks.
- Find an absolute minimum and absolute maximum,find a local minimum and local maximum, find the second derivative, and find the point of inflection show all work y= x-sinx, 0 less than or equal to x less than or equal to 2pieFind the critical points of the function. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails). f (x, y) = x ln(x + y)How do I solve the derivative for x to find the critical points and identify the absolute minimum and maximum?
- We have two approaches to classifying critical points as local minima or maxima: the first derivative test and the second derivative test. In what situations is the second derivative test easier to use than the first?find the critical numbers of (if any), (b)find the open interval(s) on which the function is increasing ordecreasing, (c) apply the First Derivative Test to identify allrelative extrematake the derivative of this function - find the critical points in order to find the maximum and minimum values for your function - prove that the critical points represent maximum or minimum points (eg: with an interval table) - find the extreme points on your function Using this info Problem: An open-top cylindrical tank with a volume of 2000 cubic meters is to be constructed using steel. The steel used for the top and bottom costs 0.5 dollars per square meter, while the steel used for the sides costs 0.3 dollars per square meter. Determine the dimensions of the tank that will minimize the cost of steel used. arrow_forward Step 3: State the variables of the problem Variables: r: radius of the base of the cylinder in meters h: height of the cylinder in meters Function: The surface area of the cylindrical tank is given by: A = 2πrh + 2πr2 The cost of steel is given by: C = 0.5(2πr 2) + 0.3(2πrh) Objective: Minimize the cost of steel C. Domain: r and h must be positive…
- The base of a rectangular box, open at the top, is to be three times as long as it is wide.Find the dimensions of the box with minimal surface area if the volume of the box is to be 2250 cubicinches. Show and organize your work; use the first derivative test or the second derivative test orother tools to check that yours is the desired optimal solution.Find the critical points, use the second derivative test, and determine the relative maximum and minimum for each critical point found. y = 6√x - xfind the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the first derivative test to identify all relative extrema