What is the lagrangian multiplier technique

A simple and elegant method of finding local minima or local maxima of a function subject to equality or inequality constraints.

The "Lagrange multipliers" technique is a way to solve constrained optimization problems. Super useful!

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Horizontal asymptote at  tells us that the original graph has been translated down.since  ,  are positive.  also we can say that the point  has a smaller  -coordinate than  .this means that the  transformed exponential function is increasing as it goes to the right. as it goes from  to , the value of the exponential function increases. it goes from to something bigger, . therefore, as  . the left hand would be the side that approaches the horizontal asymptote.so the answer is d