1. ## Finding f

I need help getting the antiderivative.

Find f.

f '(x)= (3x + sqrt(x) + 4)/(x^2); f(1)= -1

I got: f '(x)= 3/x + 1/x^(3/2) + 4/x^2

I broke it up so each piece is under x^2.

Is this wrong?

2. ## Re: Finding f

Just need to integrate each by the addition and power rules; then plug in the f(1)=-1.

3. ## Re: Finding f

Getting the antiderivative from my reduced equation is what I need help getting

4. ## Re: Finding f

What you have done is in the right direction, I would write:

$\displaystyle f'(x)=3x^{-1}+x^{-\frac{3}{2}}+4x^{-2}$

Now use the power rule for integration term by term, then use the given point (1,-1) to determine the constant of integration, or use the boundaries as limits for definite integrals. The first method is probably more familiar.

5. ## Re: Finding f

For the integral I got F(x)= 3lnx - 1/(1/2sqrt(x)) - 4/x

I keep getting this. I dont believe for it to be right?

6. ## Re: Finding f

Yes, that's right (but don't forget the constant of integration), I would write this as:

$\displaystyle f(x)=3\ln(x)-\frac{2}{\sqrt{x}}-\frac{4}{x}+C$

Now, use $\displaystyle f(1)=-1$ to find $\displaystyle C$.

7. ## Re: Finding f

Okay. I got C = 5. So now I believe the equation is:
F(x)= 3lnx - 2/sqrt(x) - (4/x) + 5

Is this the correct format to write in?

8. ## Re: Finding f

Yes, that's correct, although you don't need the parentheses around 4/x, but they don't make it incorrect.

9. ## Re: Finding f

I just did that so you can see its together. Thank you!