1. ## f(4)=?

Consider the function f(x) whose second derivative is f(x)=2x+9sin(x). If f(0)=4 and f(0)=4, what is f(4)?

I don't know what i'm supposed to know given f(0) and f'(0). Help please.
Is it giving me the C value when i take the anti derivative? =/

2. Originally Posted by Raj
Consider the function f(x) whose second derivative is f(x)=2x+9sin(x). If f(0)=4 and f(0)=4, what is f(4)?

I don't know what i'm supposed to know given f(0) and f'(0). Help please.
Is it giving me the C value when i take the anti derivative? =/
When you take the indefinite integral of your function, in each case, you will be left with an unknowns constant. Use the given information to determine the constant.

3. Originally Posted by Raj
Consider the function f(x) whose second derivative is f(x)=2x+9sin(x). If f(0)=4 and f(0)=4, what is f(4)?

I don't know what i'm supposed to know given f(0) and f'(0). Help please.

$\displaystyle f'(x)=\int f''(x)dx\,,\,f(x)=\int f'(x)dx$...but there is that annoying integration constant every time, so the given data helps you to find what exactly are those constants and thus know completely the function.

Tonio