The tangent to the curve y=ex drawn at the point c,ec intersects the  line joining the points c−1,ec−1 and c+1,ec+1

Equation of straight line joining Ac+1,ec+1 and Bc−1,ec−1 is y−ec+1=ec+1−ec−12(x−c−1)-----1 Equation of tangent at c,ec is y − ec  =  ec (x−c)----2Subtracting (1) from (2),  we getec(e−1)=ec(x−c)−12e−e−1(x−c)+12e−e−1⇒12e+e−1−1=(x−c)1−12e−e−1⇒x−c=e+e−1−22−e+e−1<0∴e+e−1>2 and 2+e−1−e<0⇒x