Question

Find all points on the graph of the function f(x) = 2 cos(x) + (cos(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

I have pi/2 and 3pi/2 for x values. But when I plug them I get zero. Is this correct as y values or am I solving it wrong? I took the derivative and set it equal to zero. But I believe I am wrong. Help urgent!

Answer 1

well, from the graph at

http://www.wolframalpha.com/input/?i=+2+cos%28x%29+%2B+%28cos%28x%29%29^2

I'd say you were wrong.

f = 2cosx + cos^2(x)
f' = -2sinx - 2sinx cosx
= -2sinx(1+cosx)
f'=0 where sinx=0 or cosx = -1
x = 0 or pi