More graphing ?Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use a graphing utility to check your work. f?? ?)= ?? ?3(?x? ? 2)2

Solution:- Step1 Given function is 1 2 f(x)= x (x 2) And the domain of given function is [-, ] The given function is not symmetrical about x-axis and y-axis and not from origin. Step2 Differentiate the given equation to find f’(x) we get, 3 (x2)2 f’(x)= 2(x-2) x + 2 3x3 (x2)(7x2) = 2 3x3 Again differentiate f’(x) to find f”(x) we get, 7x2 2(x2)(7x2) 7(x2) f”(x)= 2 - 5 + 2 3x3 9x3 3x3 2 = 28x 16x8 9x3 Step3 To get extreme value we have to use f’(x)=0 (x2)(7x=0 3 3x (x-2)(7x-2)=0 2 x=2, x= 7 These are the critical points. Step4 To find the inflection points we have to use f”(x)=0 28x 16x8 5 =0 9x3 2 28x 16x 8=0 2 4(7x 4x 2) = 0 7x 4x 2=0 x= 2±32...