Integrals

Suppose f″(x)=−36sin(6x) and f′(0)=−3, and f(0)=−6.
Find, f(π/4)=

Question

Integrals

Suppose f″(x)=−36sin(6x) and f′(0)=−3, and f(0)=−6. 
Find, f(π/4)=

consliver19 · Answer

I guess what I'm asking is, do I take the antiderivative, and plug in the value of the previous derivative? I dont know if this makes sense.. sorry,

danjs · Answer

yes, recall when you take an integral how it has the +C  constant that is included?

danjs · Answer

Those given points are the conditions to figure out what the constant will be.

danjs · Answer

$$\large f'(x)= \int\limits -36\sin(6x)dx = 6 \cos(6x)+C$$

That is a family of curves for f'(X) depending on what C is. They give you a point f'(0)=-3 that is on the f'(x)

f ' (x) = 6cos(6x) + C
-3  =  6cos(6*0) + C
C=-9

so   f ' (x) = 6xos(6x) - 9

danjs · Answer

same thing to get the function y

consliver19 · Answer

Yo, sorry for the super late response but thanks! Does the # term derivative matter at all?

likeabossssssss · Answer

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