Complete parts a. and b. below. a. Prove that f(x)=x- In x is increasing for x> 1. First, find the derivative. f'(x) = What property of the derivative can be used to show the function is increasing? OA. The derivative approaches to one as x approaches infinity. OB. The derivative is decreasing for x> 1. OC. The derivative is positive for x> 1. OD D. The derivative is undefined at x = 0. b. Using part (a), show that In x1. What can be said about f(x) if it is increasing for x>1? OA. The value of x is increasing, but the value of In x is decreasing. OB. The value of x is growing at the same rate as In x. OC. The difference between x and In x is getting smaller. OD. The difference between x and In x is growing larger. How does this show that Inx1? *** OA. If the value of x is growing at the same rate as In x, then the curves are parallel, where x is greater than In x. OB. If the difference between x and In x is increasing, then x must be greater than In x.

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