Question

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

Answer 1

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.

Answer 2

ok with that?

Answer 3

Not fully

Answer 4

which part are you unhappy with?

Answer 5

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

Answer 6

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.

Answer 7

Oh, I get it now thank you.

Answer 8

yw