Question #1989
Find f.
f '' (x) = 3 - 7x - 38x3
f(0) = 1
f '(0) = 4
f(x) = ___________________
f '' (x) = 3 - 7x - 38x3
f(0) = 1
f '(0) = 4
f(x) = ___________________
Expert's answer
Let's integrate f'':
f' = 2x - 7/2 x2 - 19/2 x4 +C1
Since f'(0) = 4 C1 = 4
f = x2 - 7/6 x3 -19/10 x5 +4x + C2
f(0) =1 , C2 = 1
f(x) = x2 - 7/6 x3 -19/10 x5 +4x + 1.
f' = 2x - 7/2 x2 - 19/2 x4 +C1
Since f'(0) = 4 C1 = 4
f = x2 - 7/6 x3 -19/10 x5 +4x + C2
f(0) =1 , C2 = 1
f(x) = x2 - 7/6 x3 -19/10 x5 +4x + 1.
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#340153 on Dec 2023
#340153 on Dec 2023