Homework Help: math

Posted by weloo_volley on Tuesday, May 8, 2012 at 6:18pm.

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^3-3x^4 on the interval [-2,2] .

math - Reiny, Tuesday, May 8, 2012 at 7:04pm
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 + (π-72)/18

Answer this Question

Related Questions

math - Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of ...
math - help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...
math - help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...
math - Question-2; Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...
calculus - Consider the function y=x/(x+1) a) Find dy/dx b) Find the equation of...
Math--Calculus - Let y = f(x) be the continuous function that satisfies the ...
Calculus - 1. a) For the Function and point below , Find f’(a). b) ...
Calculus - 1. a) For the Function and point below , Find f’(a). b) ...
Calculus - 55. Find an equation of the tangent line to the graph of f(x) =x^3 - ...
calculous - 3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the ...

For Further Reading

First Name:
School Subject:
Answer: