Page2of 12PROBLEM ONE: FUNCTION ANALYSIS REVERSEDFor this problem, we'll make it a little bit trickier - you'll need to work backwards from some information to figure out what the function is.Suppose f(x) is a function in the form f(x)=AxBe2x. The following is known about f(x) :f is decreasing on (-,0)f is increasing on (0,)-f(1)=-3e2Step 1: Start by getting the expression for f'(x) in terms of A and B. Use Symbolab to simplify (and make sure it's correct) but do at least show the quotient rule setup to start.Step 2: With the information given and the expressions you have for f and f' you have everything you need to solve for A and B. Do so (show all the steps of your solution process) and write the expressions for the functions. If you can't get this step, let me know and I'll "sell" it to you for just a few points off so you can keep going in the problem.F2F3F4F5F6F7F8F9F10F11Page3of 12Step 3: Finish off the function analysis. This function has a domain of all reals, and hence no VA's or holes, but it does have a horizontal asymptote. Give the equation of the horizontal asymptote, supported by the appropriate limit calculation (including L'Hospital).Step 4: And now discuss the concavity. Get f''(x), solve for PIPs, sign test, and state the intervals where f is concave up, and f is concave down.Page4of 12Step 5: We'll skip the x|y| what table since there's not much else to work out other than the y value for the inflection point. So to finish it off, make a nice Desmos graph. Be sure to put all key features on the graph, and LABEL them appropriately on the graph. Look in past function analyses for the tags we use to describe points of interest.PROBLEM TWO: OPTIMIZATIONWhat point on the graph of f(x)=ln(3x-1) is closest to the point (8,-2)? The graph shows the setup: imagine a line segment connecting an arbitrary point (a,f(a)) on the f(x) curve to the fixed point (8,-2) and the goal is to minimize the length of the segment. Give the coordinates of the point closest to (8,-2) and the minimum distance (length of segment).Page4of 12PROBLEM TWO: OPTIMIZATIONWhat point on the graph of f(x)=ln(3x-1) is closest to the point (8,-2)? The graph shows the setup: imagine a line segment connecting an arbitrary point (a,f(a)) on the f(x) curve to the fixed point (8,-2) and the goal is to minimize the length of the segment. Give the coordinates of the point closest to (8,-2) and the minimum distance (length of segment).Set up the function. This is just the distance formula between the two points, customized for that particular f(x). With distance questions, it's common to minimize the square of the distance; i.e. set it up as d2= and then don't bother to solve for d=s2tuff , since whatever value minimizes d2 also minimizes d. If you want me to check this step for you before proceeding, just ask. If you can't get the setup at all, I'll sell it to you for a couple points so you can keep going.Take the "distance squared" function through the full optimization process. This should follow the steps outlined in the lecture notes - be sure to label each step clearly, including the step where you do some sort of test that verifies whether each critical value is leading to a local minimum or maximum (be smart about this and use something like Desmos that will give derivative values without you needing to write out the derivative function). I recommend using Wolfram to solve for the critical values; round to two places. Hint: at the end, make a final determination about the answer - there could be multiple local minima or dips in the distance function, but there's only one closest point.Answer clearly at the end everything the question asks for, using sentences.Page5of 12(space for the steps)Your sentence(s): Hello Could anyone solve all of that please i need it fast please