Re: Problem finding maximum

*To*: mathgroup at smc.vnet.net*Subject*: [mg127583] Re: Problem finding maximum*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sun, 5 Aug 2012 02:34:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120805014915.A5ED5684F@smc.vnet.net>

f[x_, a_] = (a^3 - 6 x - a^2 (4 + x) + a (2 + 12 x - 4 x^2))/(8 a); aa1 = .7481; Plot[Abs[f[x, aa1]], {x, 0, aa1}] "FindMaximum[f, x] searches for a local maximum in f, starting from an automatically selected point." FindMaximum[{Abs[f[x, aa1]], 0 <= x <= aa1}, x] {0.0317268, {x -> 0.7481}} "FindMaximum[f, {x, x0}] searches for a local maximum in f, starting from the point x = x0." FindMaximum[{Abs[f[x, aa1]], 0 <= x <= aa1}, {x, .1}] {0.0540933, {x -> 1.*10^-7}} You just needed to give it a better starting value than the default. Alternatively, use NMaximize "NMaximize always attempts to find a global maximum of f subject to the constraints given." NMaximize[{Abs[f[x, aa1]], 0 <= x <= aa1}, x] {0.0540933, {x -> 0.}} Bob Hanlon On Sat, Aug 4, 2012 at 9:49 PM, Cisco Lane <travlorf at yahoo.com> wrote: > I cannot seem to find the corrrect maximum for the absolute value of the following function in 0<=x<=aa1 > > aa1 = .7481 > > f[x_, a_] = (a^3 - 6 x - a^2 (4 + x) + a (2 + 12 x - 4 x^2))/(8 a) > > For example, FindMaximum[{Abs[f[x, aa1]], 0 <= x <= aa1}, x] gives {0.0317268, {x -> 0.7481}} > > The correct answer is at x=0, where Abs[f[0,aa1]]=0.0540933 but I have tried every maximization function I can think of and nothing will give me the correct answer. Can anyone help? >

**References**:**Problem finding maximum***From:*Cisco Lane <travlorf@yahoo.com>