Find f if f′′(x)=sinx+cosx, f′(0)=4, and f(0)=5

find f(x)
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I got the integral and (double?) integral: -cosx+sinx and -sinx-cosx respectivly. I have no cluee how to solve the rest here. I got it with another similar problem but how do i do it with 2 integrals?

Question

Find f if f′′(x)=sinx+cosx, f′(0)=4, and f(0)=5

find f(x)
------------------------------

I got the integral and (double?) integral: -cosx+sinx and -sinx-cosx respectivly. I have no cluee how to solve the rest here. I got it with another similar problem but how do i do it with 2 integrals?

misty1212 · Answer

you are missing the constants which you find like before

misty1212 · Answer

$$f'(x)=-\cos(x)+\sin(x)+C$$ and you need $C$ via 
$$f'(0)=4$$

anonymous · Answer

hey misty sorry im not so good at these lol 

so i would need to to plug (0) into x and set it equal to 4
right?

misty1212 · Answer

yes, just like the other one
no need to be sorry though

anonymous · Answer

so i would have 5=C correct? for the first part?

anonymous · Answer

would this mean I would have -sinx-cosx+5x=f(x)?

misty1212 · Answer

$$4=-1+C\
C=5$$ ok good

misty1212 · Answer

and yes but don't forget the +C 
you have to do this dog an pony show again

misty1212 · Answer

$$f(x)=-\cos(x)-\sin(x)+5x+C$$ etc etc

misty1212 · Answer

i have a question

misty1212 · Answer

why don't you use this one?

anonymous · Answer

lol I think I will

anonymous · Answer

but one more question

anonymous · Answer

So I ended up with 6=C for f(x) but I feel that is eerily wrong

misty1212 · Answer

lets check

misty1212 · Answer

$$f(x)=-\cos(x)-\sin(x)+5x+C$$
$$f(0)=-1+C=5\
C=6$$ what is wrong with that ?q

anonymous · Answer

...Nothing? i think?