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

Textbook Question

Chapter 4, 4.9 - Problem 47 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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`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`

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