An exotie curve (Putnam Exam 1942) Find the coordinates of four local maxima of the function and graph the function for 0 ? ?x? ? 10.

Solution 78AE Step1 Given that x f(x)= 1+x sin x The domain of the graph is 0 x 10 For maxima The maximum will be when the denominator is in its minimum Now, x sin x is a square term, so, the minimum of denominator will be 1 So, for minimum 2 1+x sin x 1 (x sin x) 0 3 x sin x 0 This is possible when x=0 or sin x=0 Now, the general solution of Sin x=0 is x=n Here n is an integer and 3.14 Another solution for numerator near 4 So, x= = 3.14=0.79 4 4 Step2 Now at x=n and n=1 x==3.14 At n=2 x=2=2*3.14 = 6.28 So, the local maxima are at...