Question

What is the maximum value of the function f(x)= 12 - 3sin (3pi/2 x)

Answer 1

The lowest value of sinα is -1.

When x=1, you get:

$f\left( x \right) =12-3\sin { \left( \frac { 3 }{ 2 } \pi \right) } \\ \\ =12-3\left( -1 \right) \\ \\ =12+3\\ \\ =15$

So the maximum value of the function is 15.

Answer 2

F(x) = 12 - 3sin(3π/2x)
f(x) = 12 - 3sin(9.42/2x)