1. Questions

Calculus

I have the equation:
cos x - x = f(x)
I am told to find the relative extrema. I am also told to use the Second Derivative Test where applicable.
My question is how do I solve this problem, and how do I know when to use the Second Deriv test?
Thanks!

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Phil

  1. Points where the first derivative is zero are relative maxima if the second derivatve is negative and relative minima if the second derivative is positive.

    In your case, df/dx = 0 when f'(x) = -sin x -1 = 0; sin x = -1
    That happens when x = 3 pi/2.
    At that point, f''(x) = -cos x = 0

    So the second derivative fails to show if is a maximum or minimum. 3 pi/2 could be an inflection point, where the curve flattens out and then resumes its downward trend

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    drwls

  2. Can't i figure out if its increasing or decreasing using the first derivative test?
    What is the point of the second derivative test?

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Phil

Respond to this Question

First Name

Your Response

Similar Questions

  1. Mathmatics

    Find equation of tangent to curve at given point. x=cos(t)+cos(2t) y=sin(t)+sin(2t) (-1,1)

  2. Calculus (Related Rates)

    The position of a particle moving in a straight line is given by s(t) = (e^(-t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation: cos(5T) = 0 5T =

  3. Pre-Cal

    Find sin 2x, cos 2x, and tan 2x from the given information. [1]. sin x = 8/17, x in Quadrant I 1). sin 2x =________. 2). cos 2x =________. 3). tan 2x =________. [2]. sin x = -5/13, x in Quadrant III 1). sin 2x =________. 2). cos

  4. Math

    The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0

  1. Trigonometry

    Find the exact solutions of the equation in the interval [0, 2π). (cos 2x) - (cos x)=0

  2. Studying for Pre Cal exam

    Find the fourth roots of − 1/2 + (square root)3/2 i Write the roots in trigonometric form. A - w 1=cos(35°)+isin(35°) w2 =cos(125°)+isin(125°) w3 =cos(215°)+isin(215°) w4 =cos(305°)+isin(305°) B - w1

  3. Trigonometry

    Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) cos(x+3pi/4) - cos(x-3pi/4) = 1

  4. Math

    Suppose f(x) = sin(pi*cosx) On any interval where the inverse function y = f –1(x) exists, the derivative of f –1(x) with respect to x is: a)-1/(cos(pi*cosx)), where x and y are related by the equation (satisfy the equation)

  1. self-study calculus

    Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I -cos(t)j+sin(t)k I don't know what to do. I let x=cos(t), y=-cos(t) and z= sin(t). Should I let t be any

  2. Algebra

    Write an equation for the translation of the function. y = cos x; translated 6 units up A. y = cos x- ­ 6 B. y = cos(x + 6) C. y = cos x + 6 D. y = cos(x ­ 6) I think its B or c..

  3. trig

    Find all solutions to the given equation in the interval [0,2π). Give the exact solution, including "pi" for π. For any unused answer boxes, enter DNE in all capital letters. (a) 2cos x=2 so cos x=1 =0..(now what?) (b) 4cos

  4. Pre calc

    Find all primary solutions (i.e. 0 ≤ θ < 2π ) of the equation cos(2θ ) = 4 − 3 cos(θ ). Find all primary solutions (i.e. 0 ≤ θ < 2π ) of the equation cos(2θ )cos(θ ) = sin(2θ )sin(θ ). Please can somone help and

View more similar questions or ask a new question.