`f''(x) = x^(-2), x>0, f(1) = 0, f(2) = 0` Find `f`.

Expert Answers
hkj1385 eNotes educator| Certified Educator

`f''(x) = x^-2`

`f'(x) = -x^-1 + a`

`f(x) = -lnx + ax + b`

`Now, f(1) = f(2) = 0`

`thus, a + b = 0`

`and , -ln2 + 2a + b = 0`

`thus, a = ln2 `

`b = -ln2`

`thus, f(x) = -lnx + xln2 - ln2`

``

` `

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question