Question

Find f(x) from the given information? f''(x)=6x, f(1)=5, f(3)=17

Find the function f(x) from the given information:
f''(x) = 6x
f(1) = 5
f(3) = 17

Answer 1

`f(x) = x^3-7x+11`

Explanation:

We have:

`f''(x)=6x`

Integrating we get:

`f'(x)=3x^2+A`

Integrating again we get:

`f(x)=x^3+Ax+B`

Using the initial condition we have:

`f(1)=5`
`\ \ \ => 1 + A+B = 5`
`\ \ \ => A+B=4` ..... [A]

`f(3)=17`
`\ \ \ => 27+3A+B=17`
`\ \ \ => 3A+B = -10` ..... [B]

And solving these simultaneous equations [A] and [B] we have:

`A = -7` and `B=11`

Leading to the solution:

`f(x) = x^3-7x+11`