💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# Find $f$.$f"(t) = t^2 + 1/t^2$, $\quad t > 0$, $\quad f(2) = 3$, $\quad f'(1) = 2$

## $$f(t)=\frac{t^{4}}{12}-\ln (t)+\frac{8}{3} t-2.97$$

Derivatives

Differentiation

Volume

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

### Video Transcript

So we're given that F double crime X is equal to X squared plus one over expert. What can we expect the negative too. Then we have that the F prime of X is going to end up giving us X cubed over three minus X, the -1 or -1 over X. Then that's me plus C. But we know that when X is equal to one, we'll end up getting to start going to give us uh eight thirds, then F of X, We'll end up giving us X to the 4th over 12 minus the natural log of X Plus 8/3 acts. And then when we have plus C and we evaluate it, we end up getting a negative 2.97. So that's our final answer.

California Baptist University

#### Topics

Derivatives

Differentiation

Volume

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp