SOLUTION: Find a function f that satisfies the conditions. f ''(x) = x2, f '(0) = 4, f(0) = 2 f (x) = ?

Algebra ->  Equations -> SOLUTION: Find a function f that satisfies the conditions. f ''(x) = x2, f '(0) = 4, f(0) = 2 f (x) = ?      Log On


   

Question 287534: Find a function f that satisfies the conditions.
f ''(x) = x2, f '(0) = 4, f(0) = 2
f (x) = ?
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
f''(x) = x^2,
f'(x) = (1/3)x^3+C..... f'(0)=4 ---> 4=(1/3)(0)^3+C ---> C=4 ----> f'(x)=(1/3)x^3+4


f(x) = (1/12)x^4+4x+D

2 = (1/12)(0)^4+4(0)+D


2 = 0+D

D = 2


Answer: f(x) = (1/12)x^4+4x+2