y'=e^xcosx -e^xsinx

=e^x(cosx-sinx)

y''=e^x(cosx-sinx)+e^x(-sinx-cosx)

=-2e^xsinx

When the image of y''>0, y = e x cosx function is concave upward, the minimum value may be obtained at this time.

∵e^x>； 0

∴sinx<； 0

2kπ+π& lt； x & lt2kπ+2π

The angles are in the third and fourth quadrants.

y'=0

∵e^x>； 0

∴cosx-sinx=0

tanx= 1

x=kπ+π/4

The angles are in the third and fourth quadrants.

∴x=(2k+ 1)π+π/4 to get the minimum value.