Prove that the geometric mean of two real numbers a and b, is greater than or equal to the harmonic mean of a and b.

Note that the inequality is only true when a and b are both the same sign (because the geometric mean requires a×b to be positive).

This allows us to take the square root of the inequality in step 6 without worrying about a negative radicand.

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.