math
posted by weloo_volley on .
weloo.
Consider the function f(x)= cos3x 4sin3x.
(a)Find the equation of the line normal to the graph of f(x) when x= pie/6 .
(b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal.
(c)Find the absolute extrema of the function f(x)=5+6x^33x^4 on the interval [2,2] .

You are not "dumping" homework on us, are you?
I will do the first one, you do the others and let me know what you got
a)f(x) = cos 3x  4sin 3x
f'(x) = 3sin(3x)  12cos(3x)
the slope of the tangent when x=π/6
= 3sin(π/2)  12cos(π/2)
= 3  0 = 3
so the slope of the normal is 1/3
when x=π/6
f(π/6) = cos π/2  4sin π/6 = 0  4 = 4
We need the equation of a line with slope 1/3 and a point (π/6, 4) on it
using y = mx + b
4 = (1/3)π/6 + b
b = π/18  4 or (π  72)/18
y = (1/3)x + π/18  4 or y = (1/3)x + (π72)/18