f(x)=4√3cos²x+√3-4sinxcosx
=2√3﹙1+cos2x﹚-2sin2x+√3
=4[﹙√3/2﹚cos2x-﹙1/2﹚sin2x]+3√3
=4cos﹙2x+π/6﹚+3√3
∵π/4≤x≤7π/24
∴﹙2/3﹚π≤2x+π/6≤﹙3/4﹚π
由图像可知在﹙3/4﹚π处最小
∴此时x=7π/24
f(x)=4√3cos²x+√3-4sinxcosx
=2√3﹙1+cos2x﹚-2sin2x+√3
=4[﹙√3/2﹚cos2x-﹙1/2﹚sin2x]+3√3
=4cos﹙2x+π/6﹚+3√3
∵π/4≤x≤7π/24
∴﹙2/3﹚π≤2x+π/6≤﹙3/4﹚π
由图像可知在﹙3/4﹚π处最小
∴此时x=7π/24