Calculus

posted by .

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 y-value (x,y)=

larger y-value (x,y)=

  • Calculus -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. 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/x-5 (x, y) = (smaller x-value) (x, y) = (larger x-value)
  3. 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)
  4. 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 comma-separated list.) y = sin x/ 2 + cos x
  5. Calculus (Help)

    The graph of y=cos x * ln cos^2x has seven horizontal tangent lines on the interval [0,2pi]. Find the x-coordinate of all points at which these tangent lines occur. What the derivative of the function?
  6. Calculus (Help)

    The graph of y=cos x * ln cos^2x has seven horizontal tangent lines on the interval [0,2pi]. Find the x-coordinate of all points at which these tangent lines occur. What the derivative of the function?
  7. Calculus

    Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 15x2 (x, y) = ( , ) (smaller x-value) (x, y) = ( , ) (larger x-value)
  8. 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)
  9. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  10. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/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 …

More Similar Questions