If a<(28)13−3

Let f(x)=x13,x∈[27,28]Differentiating with respect to x  on both sides⇒f'x=13x23 By Lagrange's Mean value theorem: f(b)−f(a)b−a=f′(c), where c∈(27,28)⇒(28)13−(27)1328−27=f′(c)⇒(28)23−3=13c23 Now, 271c23>12823⇒127>13.c23>13(28)23=(28)133128>128∴128<13(c)23<127⇒128<(28)13−3<127