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- Find the local maximum and minimum values of f using both the first and second derivative tests. f(x) = x2 / (x - 1) *please use handwriting not typing, I understand it better that way*2. Consider the function f(x) = x^2 -x +1 / x^2+1 If you were asked to find all the relative extrema of the function, would you prefer using the first or second-derivative test? Explain your reasoning.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.
- valuate the second derivative of the function at the given point. Use a computer algebra system to verify your result.using the derivative definition how do I find f(x) = -6(square root over x).15. Describe the First Principle method and the Power Rule method for finding the derivative. Which method do you refer and why?
- assume the acceleration of the object is meters per second per second. (Neglect air resistance.) A baseball is thrown upward from a height of 2 meters with an initial velocity of 10 meters per second. Determine its maximum height. SHOW ALL THE STEPS: INCLUDING Algebraical, formulas, etctake 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 number each one in bolded 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.…determine the equation of the quartic function below no calculus, grade 12 advanced funtions
- A farmer wants to fence in 800 ?t2 of land in rectangular plot to be used for different types of shrubs. The plot is to be divided into four equal plots with three fences parallel to the same pair of sides. What is the least number of feet of fence needed? Use derivative and second derivative test method within your solution.take 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…limit