maths need help

using the interval [0,2pi]
and f(x) = sinx + cosx, obtain c £ (0,2pi) that satisfies the conclusion of Rolle's theorem
where £ mean element of and C means number
show step

  1. 👍
  2. 👎
  3. 👁
  1. f(0) = f(2π) = 1
    so the condition is satisfied.

    So, now you want c such that f'(c)=0

    f' = cosx - sinx
    f' = 0 at x = π/4
    π/4 is in the interval [0,2π], so ta-da!

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Precalculus

    Solve for x given the interval of [0,2pi). cos^2x=2+2sinx I got (3pi)/2 or 270 degrees.. By the way, does the notation [0,2pi) mean 0

  2. trigonometry

    how do i simplify (secx - cosx) / sinx? i tried splitting the numerator up so that i had (secx / sinx) - (cosx / sinx) and then i changed sec x to 1/ cosx so that i had ((1/cosx)/ sinx) - (cos x / sinx) after that i get stuck

  3. maths

    (Sin^3x-cos^3x)/(sinx-cosx) – cosx/sqrt(1+cot^2x)-2tanxcotx=-1 where x∈(0,2pi) general value of x.

  4. Trigonometry

    4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0

  1. calculus

    find all extrema in the interval [0, 2pi] if y=sinx + cosx and also a certain item sells for $30. if the cost of producing this item is given by C=.05^3 + 100, find the mariginal profit when x=10.

  2. trig

    Find all solutions of the equation 2sin^2x-cosx=1 in the interval [0,2pi) x1= ? x2=? x3=?

  3. Math

    How many solutions does the equation cosx + 1/2 = 1 have for 0

  4. ms sue! Algebra help

    What are the graphs of y = cos x and y = sec x in the interval from -2pi to 2pi?

  1. advanced functions

    Determine approximate solutions for this equation in the interval x is all real numbers [0, 2pi), to the nearest hundredth of a radian: cosx + 0.75 = 0

  2. Algebra 2

    Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

  3. Calculus

    The function g(x)=12x^2-sinx is the first derivative of f(x). If f(0)=-2, what is the value of f(2pi)? a)30pi+2 b)8pi^2-2 c)4pi^3+8 d)32pi^3-2 e)2pi^2+5

  4. Simplifying with Trigonometry Identities

    Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each

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