Find the value of x when S is a local minimum, justifying that it is a minimum
S=2(π-2sinx)

Question

Find the value of x when S is a local minimum, justifying that it is a minimum 
S=2(π-2sinx)

anonymous · Answer

dS/dx =  -4 cos x = 0   at critical point
cos x = 0
x = pi/2
d2s/dx^2 =  -4 * - sin x = 4 sin x
4 sin pi/2 is positive ( =4)  so  s is a minimum at x = pi/2.

anonymous · Answer

ok with that?

anonymous · Answer

Not fully

anonymous · Answer

which part are you unhappy with?

anonymous · Answer

The d then how did pi disapear. (mostly the first part)

anonymous · Answer

oh ok - sorry to be so long replying
dS/dx  means the derivative of S with respect to x  
pi is a constant and the derivative of a constant is zero

ds/dx gives the slope of the tangent to the curve. this equals 0 at a critical (turning) point.
eg maximum, minimum or point of inflection.

anonymous · Answer

Oh, I get it now thank you.

anonymous · Answer

yw