Hi there could you please guide me in the right direction for this question:

The graph y=12sin(PI/5)x gives the height in cm of a piston above the centre axis (x) seconds after being trned on.

A) State the minimum and maximum displacement of the piston from the centre axis.

By sin(PI/5)x do you mean

x sin(PI/5)

or sin[(PI/5)x] ?


At Minimum values, dy/dx = 0 and d^2y/dx^2 > 0


At Maxmum values, dy/dx = 0 and d^2y/dx^2 < 0

Hence make dy/dx = 0 and find corresponding values of x.

At these values, compute d^2y/dx^2. When this is negative, you have a Maximum
and when this is positive you get a Minimum.

However, remember, that mathematical Maximum and Minimum do not necessarily correspond to the Greatest and Least respectively.