Math

Can you help me with this? I did this many times and got different answers each time.

Find f.
f ''(x) = 3e^x + 3sin(x)
f(0) = 0
f(π) = 0

My work:
f ''(x) = 3e^x + 3sin(t)
f'(x) = 3e^x - 3cos(t) + C
f(x) = 3e^x -3sin(t) + Cx + D

0=f(0)= 3e^0 - 3sin(0) + C(0) + D
D=-3

0=f(π)= 3e^π - 3sin(π) + Cπ -3
C= (3-3e^π)/π

F(x) = 3e^x -3sin(x) + (3-3e^π)/π x - 3

  1. 👍 0
  2. 👎 0
  3. 👁 258
  1. f(0) = 0
    f(π) = 0
    Check if one of them is actually f'().

    Assuming it's correct as above:
    from:
    f(x) =3e^x -3sin(x) + (3-3e^π)x/π - 3
    We get:
    f"(x)=3sin(x)+3e^x
    f(0)=0
    f(π)=0
    which clearly satisfy all the given requirements. However, since there were two initial conditions for f(x), it is possible to have multiple solutions.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    If a ball is thrown directly upwards with twice the initial speed of another, how much higher will it be at its apex? A) 8 times D) 2 times B) 4 times E) 2 times C) 2 2 times Please show any equations that are used :)

    asked by DCM on April 7, 2012
  2. Language Arts - The Odyssey - Please Check Answers

    Please help me with the following question: Read the excerpt from The Odyssey. Six benches were left empty in every ship that evening when we pulled away from death. And this new grief we bore with us to sea: our precious lives we

    asked by Brady on September 26, 2014
  3. Math

    The probability of winning a game is 20%. If you play 20 times, how many times should you expect to win? 4 times 10 times** 16 times

    asked by Reagan on April 2, 2018
  4. Algebra

    16. The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released. h= 7 cos (π/3 t) a. Solve the equation for t. (I'm pretty sure i've got

    asked by Chloe on July 7, 2018
  5. surface and volume

    A glass vase weighs 0.12lb, how much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large? possible answers; 4.32lbs 25.92lbs 0.72lbs 155.52lbs These are the last problems I have and I can't

    asked by lilman on May 1, 2012
  1. Math

    1. Simplify. 3x^2+ 5x-5x^2-4x+5-2 A.-8x^2-9x+3 B.2x^2+x+3 C.-2x^2-9x+3*** D.-2x^2+x+3 2. Add or Subtract.(8x – 2y) + (3x – 4y) A.11x+8y B.4x-y C.11x-6y*** D.5x+2y 3.(5x^2-4x-1)-(-4x^2-4) A.-9x^2-8x-1 B.9x^2-4x+3*** C.x^2-4x-3

    asked by Emma on May 5, 2016
  2. Math

    If ln a=2, ln b=3, and ln c=5, evaluate the following: (a) ln(a^−2/b^4c^−3)= -.9524 (b) ln(√b^−4*c^1*a^−1)= -1.739 (c) ln(a^2b^4)/ln(bc)^−2= 42.39 (d) (ln(c^−1))*(ln(a/b^3))^−4= -.03507 I am getting these answers

    asked by Banana on August 22, 2018
  3. Algebra 1 Foundation Concepts rewrite

    1. Write an algebraic expression for the following word phrase: the quotient of r and 12. (1 point) A)r • 12 B)r + 12 C)r ÷ 12 F)r – 12 2. Write a word phrase for the algebraic expression 3x - 7. (1 point) A)the difference of

    asked by Kitty on September 11, 2016
  4. Math

    a standard number cube is rolled 180 times. Predict how many times a 3 or 5 will be the result. 31 times 60 times 57 times 30 times I chose 31 times Is that correct i would appreciate your help

    asked by Awesome on May 13, 2015
  5. math question

    /how do i solve this? The probability of winning a game is 15%. If you play 20 times,how many times should you expect to win? A.5 times B.3 times C.6 times D.15 times

    asked by matt on June 5, 2014
  6. physics?

    In order to wake a sleeping child, the volume on an alarm clock is tripled. Under this new scenario, how much more energy will be striking the child's ear drums each second? A. twice as much B. three times as much C. approximately

    asked by tyger2020 on February 19, 2018

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