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

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

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.

I couldn't figure it out.

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?

To find the derivative function f'(x), you can differentiate the given function f(x) = 5x + 3. The derivative of f(x) represents the rate of change of f(x) with respect to x.

The derivative of f(x) can be found by applying the power rule of differentiation. For any constant c and any power n, the derivative of cx^n with respect to x is given by n * cx^(n-1).

In this case, since f(x) = 5x + 3, which can be written as f(x) = 5x^1 + 3, the derivative of f(x) is:

f'(x) = 1 * 5 * x^(1-1) = 5 * x^0 = 5

So, f'(x) = 5.

To find f(2), you need to substitute x = 2 into the function f(x) = 5x + 3.

f(2) = 5 * 2 + 3 = 10 + 3 = 13.

Therefore, f'(x) = 5 and f(2) = 13.