Using Matlab's fzero and fplot with an inline function EDUğ f = inline('exp(-4.5*x)-x/200') f = Inline function: f(x) = exp(-4.5*x)-x/200 EDUğ fplot(f,[1,2]) % generates quick plot EDUğ fzero(f,1.5) % finds root near 1.5 or if 1.5 replaced by vector Zero found in the interval: [1.02, 1.8394]. ans = 1.1469 EDUğ fzero(f,1.5,optimset('disp','iter')) %using options Func-count x f(x) Procedure 1 1.5 -0.00632912 initial 2 1.45757 -0.00587068 search 3 1.54243 -0.00674475 search 4 1.44 -0.00566619 search 5 1.56 -0.00690617 search 6 1.41515 -0.00536043 search 7 1.58485 -0.00712501 search 8 1.38 -0.00489076 search 9 1.62 -0.00741767 search 10 1.33029 -0.00413859 search 11 1.66971 -0.00780296 search 12 1.26 -0.00285213 search 13 1.74 -0.00830237 search 14 1.16059 -0.000409922 search 15 1.83941 -0.00894285 search 16 1.02 0.00505286 search Looking for a zero in the interval [1.02, 1.8394] 17 1.31583 -0.00389729 interpolation 18 1.18701 -0.00114667 interpolation 19 1.14324 0.00011458 interpolation 20 1.14722 -8.704e-006 interpolation 21 1.14694 -6.0546e-008 interpolation 22 1.14694 2.70015e-013 interpolation 23 1.14694 8.67362e-019 interpolation 24 1.14694 -1.04083e-017 interpolation Zero found in the interval: [1.02, 1.8394]. ans = 1.1469