1. Questions

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.

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

  1. To find the extrema, do the First Derivative Test.

    y = sinx + cos x
    y'= cosx - sinx
    The extrema always occur when the derivative is zero, so set it equal to zero.

    y' = cosx - sinx = 0
    = cosx = sinx
    cosx/cosx = sinx/cosx
    1 = tanx
    x = pi/4, 5pi/4

    Make a sign chart...
    y' increases on (0, pi/4) and (5pi/4, 2pi)
    y' decreases on (pi/4, 5pi/4)
    A max occurs at pi/4, a min occurs at 5pi/4.

    The extrema are...
    Relative maximum = √2 @ x = pi/4
    Relative minimum = -√2 @ x = 5pi/4

    I think you've made a mistake on your second problem. There is no variable in the C function.

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

  2. C=.05x^3+100

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

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. Math, please help

    Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secx-cosx/secs=sin^2x 1-tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1 - 2sinx Find all solutions to the equation cosx

  3. 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

  4. trig

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

  1. Calculus

    determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0

  2. Maths

    Find the general solution of equation sinx + cosx = 2 (root2) (sinx)(cosx)

  3. Calculus

    Find all points of extrema on the interval [0, 2pi] if y=x+sinx (-1.-1+(3pi/2)) (pi, pi) (-1,0) ((3pi/2), 0) none of these I got pi as my critical number but I'm confused with the intervals.

  4. Trig.......

    I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr

  1. Pre-Calc : Verify the Identity

    Verify the Identity: sin(x+π)/cos(x+3π/2) =tan^2x-sec^2x I've done: sinxcosπ+cosxsinπ / cosxcos(3π/2) - sinxsin(3π/2) sinx(-1) + cosx(0) / cosx(0)- sinx(-1) -sinx/sinx What do I do from here? Or what did I do wrong?

  2. Calculus

    1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

  3. Math

    (sinx - cosx)(sinx + cosx) = 2sin^2x -1 I need some tips on trigonometric identities. Why shouldn't I just turn (sinx + cosx) into 1 and would it still have the same identity?

  4. Calculus

    Find the relative extrema of the function f(x) = 1/2 x - sinx on the interval (0, 2 pie) please show me how you got this!!

View more similar questions or ask a new question.