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

  1. 👍
  2. 👎
  3. 👁
  1. f'(x) = 2cosx + 2sinx(cosx)
    = 0 when the tangent is horizontal

    2cosx(1 + sinx) = 0
    cosx = 0 or sinx = -1

    if cosx = 0
    x = π/2 or 3π/2
    f(π/2) = 2(1) + 1 = 3
    f(3π/2) = 2(-1) + 1 = -1
    so we have two points, (π/2 , 3) and (3π/2 , -1)

    if sinx = -1
    x = 3π/2 giving us the same point as above

    there are two points (π/2 , 3) and (3π/2 , -1)

    1. 👍
    2. 👎
  2. Thanks!!! I was getting the first point wrong!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Use this definition with the right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f(x)= 3+sin^2(x) 0

  2. calculus

    To get a better look at the graph, you can click on it. Find a function of the form f(x)=A sin(B[x−C])+D whose graph is the sine wave shown above. The curve goes through the points (−5,0) and (1,0). If needed, you can enter

  3. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

  4. calculus

    Find complete length of curve r=a sin^3(theta/3). I have gone thus- (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int

  1. calculus

    1. Find the average value have of the function h on the given interval. h(x) = 2 cos4(x) sin(x), [0, π] 2. Consider the given function and the given interval. f(x) = 6 sin(x) − 3 sin(2x), [0, π] (a) Find the average value fave

  2. d/dx

    d/dx( ln |sin(pi/x)| ) = ? Thanks. If those are absolute value signs, the derivative will not exist when sin (pi/x) = 0, because of the sign change that occurs there. Assume sin (pi/x) > 0 Let u(x) = pi/x and v(x) = sin x, and use

  3. calculus

    Determine the points in the interval (0, 2π) at which the graph of the function below has a horizontal tangent line. f(x) = 10 cos x + 5 sin 2x There should be three

  4. Calculus

    Let f be a function with second derivative given by f''(x)=sin(2x)-cos(4x). How many points of inflection does the graph of f have on the interval [0,10]? (A)Six (B)Seven (C)Eight (D)Ten (E)Thirteen

  1. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4.

  2. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with

  3. calculus

    Find the points on the curve y= (cos x)/(2 + sin x) at which the tangent is horizontal. I am not sure, but would I find the derivative first: y'= [(2 + sin x)(-sin x) - (cos x)(cos x)]/(2 + sin x)^2 But then I don't know what to

  4. math

    1)In triangle ABC, C=60 degrees, a=12, and b=5. Find c. A)109.0 B)10.4 C)11.8 D)15.1 I chose B 2)Which triangle should be solved by beginning with the Law of Cosines? A)A=115 degrees, a=19, b=13 B)A=62 degrees, B=15 degrees, b=10

You can view more similar questions or ask a new question.