Minimizing & Maximizing Functions - James C. Sutherland

!6!4!202!40!20020406080xx3+5*x2 Minimizing & Maximizing FunctionsExample: find the minimum of y=3x2 2x+1 Minima & maxima occur in Functions where the slope changes sign ( where the slope is zero). Local vs. Global min & max. Polynomials: we can find all min & max (global & local) General Functions : iterative procedure; may only find local Functions may have zero to many minima and , November 17, 2008 Min & Max of Functions - a cell containing the independent variable (x) a cell containing the function value at x, f(x). Tools the target cell to be f(x). By Changing Cells to be either max or solve NOTE: You can also use solver to solve a nonlinear equation (choose to set target cell to a value rather than min/max).10 Monday, November 17, 2008 Min & Max of Functions - a MATLAB function to evaluate f(x) given the minimum using fmin=fminsearch(fun,x0) a MATLAB function to evaluate f(x) given the minimum using fmax=fminsearch(fun,x0) 11 Monday, November 17, 2008 Many Nonlinear Equations (uncoupled)f(t)=1 exp( at)Find when f(t)= for a=[ 1].

Min & Max of Functions - MATLAB Minimization 1.Define a MATLAB function to evaluate f(x) given x. 2.Obtain the minimum using fmin=fminsearch(fun,x0) Maximization 1.Define a MATLAB function to evaluate −f(x) given x. 2.Obtain the minimum using fmax=fminsearch(fun,x0) Monday, November 17, 2008 11

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