In 2006, Fujian college entrance examination mathematics L science ninth question.

9. It is known that the function f (x) = 2sinω x (ω > 0) is in the interval [-].

π3,

The minimum value on π4] is -2, so the minimum value of ω is equal to () A.23B.32C.2D.3

Answer: b

Solution: the function period T=2π/w, so -T/4=-π/2w.

Because the minimum value of 2sinwx is -2.

So 2sinw (-π/2w+k 2π/w) =-2.

That is -π/3 ≤-π/2w+k.2π/w ≤π/4.

The solution W≥(3- 12k)/2.

Because W>0, k is an integer.

So W≥3/2

So the minimum value of w is 3/2.