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

Algebra.Com
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)   (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

RELATED QUESTIONS

Find a cubic polynomial function f(x) that satisfies both of the following conditions: (answered by htmentor)
Find an equation of a rational function f that satisfies the conditions: vertical... (answered by stanbon)
Sketch a graph of a function f that satisfies the following conditions: f does NOT... (answered by robertb)
Find the particular antiderivative that satisfies the following conditions: f''(x) = 12 (answered by Alan3354)
If a linear function f satisfies the conditions : f ( -3 ) = - 2 and f ( 3 ) = 16 , find... (answered by user_dude2008,ewatrrr)
Find an equation of a rational function f that satisfies the given conditions. vertical... (answered by greenestamps)
Given the function f(x)=x2+2x+1, find: a) f(−7) b) f(0) c) f( 1/4 ) d)... (answered by ikleyn,Edwin McCravy)
f(x) = x2 -7x + 10 Find (a) f(0),(b) F(5), and (c)f(-2) (answered by Nate)
f (x) = x2 - 7x + 10; find (a) f (0), (b) f (5), and (c) f... (answered by gsmani_iyer)