Now, let f \'\'(x) = 0 and solve for x. Remember that f \'\'(x) = 1/4 %u2212sin(
ID: 3343167 • Letter: N
Question
Now, let
f ''(x) = 0 and solve for x. Remember that
f ''(x) = 1/4%u2212sin(x/2) is a periodic function, and thus there are infinitely many angles that satisfy the condition. For this step, just give the three angles when 0 %u2264x %u2264 4%u03C0. Enter your answers as a comma-separated list.
-1/4 sin(x/2) = 0
sin(x/2) = 0
x/2 = sin - 1(0)
x = ?
Out of those three values, only x = ??? is inside the open interval (0, 4%u03C0).
We discard the others, because concavity cannot change at the terminal point of the domain of a function.
Explanation / Answer
-1/4 sin(x/2) = 0
sin(x/2) = 0
x/2 = sin ^-1(0)
=> x/2 = 0, pi, 2pi, 3pi
=> x= 0, 2pi. 4pi, 6pi
for (0,4pi), x= 0, 2pi, 4pi
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