If f'(x)=3x^2+2x and f(2)=3 then f(1)=
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Here we want to solve a differential equation, we will find that our function is f(x) = x^3 + x^2 -9

So we want to find f(x) such that we know f'(x).

We know that:

f'(x) = 3x^2 + 2x

To get f(x) we just need to integrate, we will get:

Where c is a constant of integration.

Now, we know that f(2) = 3, with that we can find the value of c.

f(2) = 2^3 + 2^2 + c = 3

          8 +  4 + c = 3

          c = 3 - 12 = -9

So the function is:

f(x) = x^3 + x^2 -9

If you want to learn more about differential equations, you can read:

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Step-by-step explanation:

We are given the derivative:

And the initial condition that f(2)=3.

And we want to find f(1).

So, to find our original function f(x), we will find the antiderivative of f'(x). Hence:

By integrating, we acquire:

Since we know that f(2)=3:

It follows that:

Therefore, our function is given by:

Therefore:

linear pair postulates