# calculus

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On the graph of f(x)=7sin(7pi x), 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

• calculus -

f(x)=7sin(7pi x) has a maginitude of 7
so the largest value is 7 and the minimum value is -7

The period is 2π/ (7π) = 2/7

so P and Q are 1/7 apart along the x-axis

for a period of 2/7 or 4/14
there is a zeros when x = 0
there is a max when x = 1/14
another zero when x = 2/14
there is a min when x = 3/14
and another zero at 4/14

so P is (1/14 , 7) and Q is (3/14, -7)

(check with your calculator, setting your mode to radians, and subbing in x = 1/14 and 3/14 )

slope PQ = (-7-7)/(3/14 - 1/14) = -14/(1/7)
= -14(7) = -98

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