A construction engineer is interested to construct a modern,hyperbolic shaped towers within the garden of a newly proposed hotel by using the hyperbolic functions, sinh x , cosh x where ?? ? ??(i) By...

A construction engineer is interested to construct a modern,hyperbolic shaped towers within the garden of a newly proposed hotel by using the hyperbolic functions, sinh x , cosh x where ?? ? ??(i) By using the definition of an increasing function, prove that the hyperbolic function sinh x is increasing.(ii) Does there exist an absolute maximum in the hyperbolic function sinh x? Prove your answer.(iii) Is (0,0) a point of inflection for the hyperbolic function sinh x? Prove your answer.(iv) Prove that for each real x = 0 , cosh x is increasing, and for each real x = 0 , cosh x is decreasing.(v) Also, prove that the hyperbolic function cosh x attains an absolute minimum at the point (0,1).(vi) Does there exist an absolute minimum in the hyperbolic function cosh x ?  Prove your answer.