irst of all, by the Intermediate Value Theorem,f(x)

f

(

x

)

has a solution in the interval(a,b)=

(3 points} Show that the function f(x} = 13 + e41 has exaotla.r one real root. First of all, by the lntermedlate 1'nr'alue Theorem, x) has a Solution In the Interval ((1.5) = {you may.r chooee an Interval of any length} Now suppose that f (x) has more than one real root. Then by the Mean 1Inl'alue 'l11eorem, between anyr pair of real roots there must be some polnt c at which f " (1,} is However, we nd me} =