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 (? )? = sin ? ? x? on[0. 2?]

Solution 23E Step1 Given function is f(x)= sin(x)-x on[0,2 ] And the domain of given function is [0,2 ] The given function is not symmetrical in [0,2 ] Step2 Differentiate the given equation to find f’(x) we get, f’(x)= cos(x)-1 Again differentiate f’(x) to find f”(x) we get, f”(x)=- sinx Step3 To get extreme value we have to use f’(x)=0 cos(x) 1 =0 Cos(x)=1 Therefore critical points are 0, 2 on [0,2 ] Step4 To get Inflection value we have to use f”(x)=0 - sin x=0 Therefore inflection point 0, 2 on [0,2 ] Step5 We have to find increasing, decreasing and concavity critical points are 0, 2 on [0,2 ] f’(x)<0 The function is decreasing The inflection points are 0, ,2 The between (0, ), f’(x)<0 f(x) has concave down The between ( ,2 ), f’(x)>0 f(x) has concave up Step6 Extreme values and inflection points. critical points are 0 and 2 At x=0 f”(x)=0 At x=2 f”(x)=0 Therefore at x=0,2 f(x) has minimum value . Step7 Asymptotes and end behavior Let f’(x)=0 x=0,2 At x=0 and x=2 f(x) then tangent parallel to x- axis lim f(x)=-2 x2 Intercepts At x=0 y=0 If y=0 x=0 Step8 Graph of given equation