Question

Please explain step by step
T(z)= sin^2(z/4), {-3 ≤ z ≤ 8}
identify the intervals where:
a) T(z) is increasing
b)T(z) is decreasing
C)T(z) is concave up
d)T(z) is concave down
Then identify the
e) absolute minimum and where it is
f) A relative maximum ( not absolute maximum and where it is

Answer 1

T'(z) = sin(z/4) cos(z/4) = 1/2 sin(z/2)
(a) T' > 0, so 0 < z < 2π
(b) T' < 0
T"(z) = 1/4 cos(z/2)
(c) T" > 0, so -3 < z < π
(d) T" < 0
(e) T = 0
(f) check where T' = 0 and T" < 0