Integration to find original function given the second derivative and coordinates?

Question

The curve $y = f (x)$ $y = f(x)$ has a stationary point at $(2, 10)$ $(2, 10)$ and it is given that $f''(x) = 12/x^3$ . Find $f(x)$

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Answer 1 · 2017-10-12T21:01:38

See below.

If $f''(x) = 12/x^3$ then $f(x) = 6/x + C_1 x+C_2$

Now we have that

$f'(2)= 0 rArr -6/2^2 + C_1=0$ and also

$f(2) =6/2+2C_1+C_2 = 10$

Solving for $C_1,C_2$ we obtain

$C_1 = 3/2, C_2 = 4$ and finally

$f(x) = 6/x+3/2x+4$