3. L'Hosptials Rule: Now that we know L'Hopital's rule, we can apply it to solve ^ more sophisticated global optimization problems. Consider domains, limits, derivatives, and values to determine the global extrema of each function f in on the given interval I. sin r (a) f(x) = I = (0, 1] 1+ cos x (b) f(x) = In x I = (1, 00] In(2r)' x3 I = [0, 00] (c) f(x) = %3D e-r

Only Need Part C

just solve c,d,e,f Part Only . No need to solve a,b.kindly used correct closed notations i.e ( , ) , [, ]

Please help me with this. Please show all your work  Calcuate the second derivative of the function - Calculate the  critical numbers for the second derivative test -intervals of concavity (based on the 2nd derivative test)

Here we will study the function f(x)  =  xe^-x , where  x ∈ [0, 10] Determine where the function is decreasing and increasing. Find all local maxima and minima. Does it have absolute (global) maxima / minima? Determine where f (x) curves up and down. Also find any turning points.

how do limits relate to derivatives and integrals? also give examples of when they are used to slove real life problems

How to find stationary points for f(x) = x^2-6x^2+9x and their local max or local min

f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on and what are the endpoints?

Car A is 80km east of Car B and begins moving west at 40km/h. At the same moment, Car B begins to move north at 70km/h. What is the closest distance in km, the cars will be from each other AND at what time t, in hours, will that distance occur?  (This is a calculus optimization problem so please show all work and include the chart of the first derivative test JUST LIKE THE EXAMPLE I AM SHOWING YOU) do it on paper pls and double check answer

Your Question: - 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, and don't use the answer that's already been posted, explain each step and label the answer like extreme points, and use a interval table for number 3  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…