f"(x)=5x+3 and f'(-2)=-3 and f(2)=-5

Question

Find f'(x) and find f(2).

Answer 1

looks like you are doing basic integration at the beginner's level.

Remember that integration is the "reverse" of differentiation.

So do this intuitively.
Ask yourself, "What terms did I have so that its derivative is 5x +3 ?"

Wouldn't that have been (5/2)x^2 + 3x + (some constant) ???

Now that would give you f'(x)
and you are given f'(-2) = 3 so you can find the constant.

Then repeat this to get f(x)

let me know what your answer is.

Answer 2

I couldn't figure it out.

Answer 3

Ok, so I got the first part done. I got 5/2 x^2 +3x -7

Now I'm stuck on the f(2)= part.

I've gotten 5/6 x^3 +3/2 x^2 -7x + C

But what do I do from there?