Conjecture Consider the functions and on the domain (a) Use a graphing utility to graph

Chapter 3, Problem 46

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Conjecture Consider the functions and on the domain (a) Use a graphing utility to graph the functions on the specified domain. (b) Write the vertical distance between the functions as a function of and use calculus to find the value of for which is maximum. (c) Find the equations of the tangent lines to the graphs of and at the critical number found in part (b). Graph the tangent lines. What is the relationship between the lines? (d) Make a conjecture about the relationship between tangent lines to the graphs of two functions at the value of at which the vertical distance between the functions is greatest, and prove your conjecture. 3xy2

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