Monday

January 26, 2015

January 26, 2015

Posted by **Kay** on Thursday, June 23, 2011 at 8:25pm.

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

- Math -
**MathMate**, Friday, June 24, 2011 at 2:53pmf(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.

**Answer this Question**

**Related Questions**

Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...

Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...

Math, please help - Which of the following are trigonometric identities? (Can be...

Calculus - Find the derivative of y with respect to x: y=3sin^4(2-x)^-1 y=[3sin(...

Calculus - How do I find the critical values? y= 4/x + tan(πx/8) What I ...

Math 2nd question - Express as a single sine or cosine function (note: this is ...

geometry/algebra - I asked this question yesterday, and I'm trying to understand...

Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...

Trig - find all solutions to the equation √3 csc(2theta)=-2 Would the ...

Math - Evaluate *Note - We have to find the exact value of these. That I know to...