Since , e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum of function.
In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex
e(h) = ∈ /h +( [tex]h^{2}[/tex]/6) M
e'(h) = - ∈ /[tex]h^{2}[/tex] + (2h/6) M
putting , e'(h) = 0
- ∈ /[tex]h^{2}[/tex] + (2h/6) M = 0
h = [tex](3 /M)^{1/3}[/tex] * (∈^(1/3))
e"(h) = 2∈ / [tex]h^{3}[/tex] + (2M)/6 equation 1
substituting value of h in equation 1, we get
e"(h) = 2∈M / 3∈ + M/3
e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum
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