For the function y = - 2+5sin (pi/12 (x-2)), what is the maximum value?

To get the function y = - 2+5sin (pi/12 (x-2)), the maximum value can be determined by differentiating the function and equating it to zero. The value of x will give the maximum value of the function.

dy/dx = 5 cos (pi/12 (x-2)) (pi/12)

dy/dx = 5 pi/12 cos (pi/12 (x-2))

Equate to zero:

5 pi/12 cos (pi/12 (x-2)) = 0

pi/12 (x-2) = 3pi/2

x = 8

Substituting,

y = - 2 + 5sin (pi/12 (8-2)

y = - 1.86