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

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)

1 Answer
Oct 12, 2017

See below.

Explanation:

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