Calculus
posted by Tim .
Find all points on the graph of the function
f(x) = 2 cos x + cos^2 x
at which the tangent line is horizontal. (Use n as your arbitrary integer.)
smaller yvalue (x,y)=
larger yvalue (x,y)=

Since the derivative is the slope of the tangent line, we need
2sinx  2cosx*sinx = 0
2sinx(1+cosx) = 0
sinx = 0 means x = nπ
cosx = 1 means x = (2n+1)π
so, f(x) has a horizontal tangent at x=nπ
Respond to this Question
Similar Questions

Math (Calculus 121)
Consider the following function. f(x) = 7x3 + x2  0.08x + 12 Find the two points on the graph at which the tangent line is horizontal. Give your values correct to 2 decimal places. ( , ) (point with smaller x value) ( , ) (point with … 
Math
Find the points on the graph of the following function where the slope of the tangent line is equal to 5/2. f(x) = x+5/x5 (x, y) = (smaller xvalue) (x, y) = (larger xvalue) 
calculus
5) Find the points on the curve below at which the tangent is horizontal. Use n as an arbitrary integer. (Select all that apply.) y=Sin(x) / 2+ Cos (x) 
calculus
Find the points on the curve below at which the tangent is horizontal. Use n as an arbitrary integer. (Enter your answers as a commaseparated list.) y = sin x/ 2 + cos x 
Calculus (Help)
The graph of y=cos x * ln cos^2x has seven horizontal tangent lines on the interval [0,2pi]. Find the xcoordinate of all points at which these tangent lines occur. What the derivative of the function? 
Calculus (Help)
The graph of y=cos x * ln cos^2x has seven horizontal tangent lines on the interval [0,2pi]. Find the xcoordinate of all points at which these tangent lines occur. What the derivative of the function? 
Calculus
Find the points on the graph of f where the tangent line is horizontal. f(x) = x3  15x2 (x, y) = ( , ) (smaller xvalue) (x, y) = ( , ) (larger xvalue) 
calculus
find the points on a graph of f where the tangent line is horizontal. f(x)= x^3  18x^2 (x,y)= (smaller x value) (x,y)= (larger x value) 
calculus
1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 
Calculus
The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(11/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals …