On the graph of f(x)=2sin(6πx), points P and Q are at consecutive lowest and highest points with P occuring before Q. Find the slope of the line which passes through P and Q.

Answer 1

for P
sin T is -1 when T = (3/4)(2pi)
= 3 pi /2

for Q
sin T then becomes +1 when
sin T = 2 pi + pi/2 = 5 pi/2
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now x for P
6 pi x = 3 pi/2
x = 1/4 and y is -2

now x for Q
6 pi x = 5 pi/2
x = (5/12) and y is +2

slope = 4/(5/12 - 1/4)

= 4 / (5/12 - 3/12)

= 4 / (1/6)

= 24