SOLUTION: Find an equation of the tangent line to the graph of f(x)= 3sin(2x)-cos(2x) at x= 3(3.14)/ 4

Algebra ->  Trigonometry-basics -> SOLUTION: Find an equation of the tangent line to the graph of f(x)= 3sin(2x)-cos(2x) at x= 3(3.14)/ 4      Log On


   

Question 1082177: Find an equation of the tangent line to the graph of
f(x)= 3sin(2x)-cos(2x) at x= 3(3.14)/ 4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of the tangent line is equal to the value of the derivative at that point.
So,
f=3sin%282x%29-cos%282x%29
df%2Fdx=6cos%282x%29%2B2sin%282x%29
So,
m=6cos%28%283%2F2%29pi%29%2B2sin%28%283%2F2%29pi%29%29
m=0-2
m=-2
At x=%283%2F4%29pi,
f=3sin%28%283%2F2%29pi%29%29-cos%28%283%2F2%29pi%29%29
f=-3%2B0
f=-3
Using the point slope form of a line,
y-%28-3%29=-2%28x-%283%2F4%29pi%29%29
y%2B3=-2x%2B%283%2F2%29pi
y=-2x%2B%283%2F2%29pi-3
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