Solve problems: 5,7,11,15,19,23,27,31,37,41,47 Determine whether each statement is true or false, and explain why.For a continuous function on a closed interval, one can determine the absolute extrema by evaluating the function at the endpoints and at each critical number.If a function on a closed interval has only one critical number at x=c, then by the critical point theorem, the function has an absolute extrema at x=c.For a function on an open interval, absolute extrema will occur at every critical number.maximum and an absolute minimum.Practice and ExplorationsIn Exercises 5-8, use the steps shown in Exercise 5 to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of the indicated expression.xy=180 and the product P=xy is as large as possible.(a) Solve xy=180 for y.(b) Substitute the result from part (a) into P=xy, the equation for the variable that is to be maximized.6.2 Exercises353(c) Find the domain of the function P found in part (b).(d) Find dPdx. Solve the equation dPdx=0.(e) Evaluate P at any solutions found in part (d), as well as at the endpoints of the domain found in part (c).(f) Give the maximum value of P, as well as the two numbers x and y whose product is that value.The sum of x and y is 140 and the sum of the squares of x and y is minimized.xy=90 and x2y is maximized.xy=105 and xy2 is maximized.ApplicationsBusiness and EconomicsHoAverage Cost In Exercises 9 and 10, determine the average cost function ?bar(C)(x)=Cxx. To find where the average cost is smallest, first calculate ?bar(C)'(x), the derivative of the average cost function. Then use a graphing calculator to find where the derivative is 0. Check your work by finding the minimum from the graph of the function ?bar(C)(x).9.C(x)=1-x32x2-3x35356Chapter 6 Applications of the Derivative47. Pigeon Flight Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead. (One possible explanation is the fact that extra energy is required to fly over water because air pressure drops over water in the daytime.) Assume that a pigeon released from a boat 1 mile from the shore of a lake (point B in the figure) flies first to point P on the shore and then along the straight edge of the lake to reach its home at L. If L is 2 miles from point A, the point on the shore closest to the boat, and if a pigeon needs 54 as much energy per mile to fly over water as over land, find the location of point P, which minimizes energy used.