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Math Question for Saturday, December 20th, 2014

Over all real numbers *x*, what is the maximum value of 4 sin 3*x* ?

**F.** 1

**G.**

**H.** 3

**J.** 4

**K.** 12

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## Correct!

**The correct answer is J.**

The maximum value for sin *X*, where *X* is any function of *x*, is 1 so sin 3*x* 1 for all *x*. Then multiplying by 4, 4 sin 3*x* 4, so the maximum value of 4 sin 3*x* is 4.

**F, G, H.** When *x* = , 4 sin 3*x* = 4 sin = 4 sin = 4 1 = 4. Since the values in F–H are less than 4, none can be the maximum value of 4 sin 3*x*.

**K.** If 12 were a value of 4 sin 3*x*, then 12 = 4 sin 3*x* for at least one value of *x*. But then 3 = sin 3*x* for at least one value of *x*. But sin 3*x* 1 for all *x*, so 12 can't be a value of 4 sin 3*x*.

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