Answer to Question #1989 in Calculus for Jess

Question

Find f.
f '' (x) = 3 - 7x - 38x3
f(0) = 1
f '(0) = 4

f(x) = ___________________

Answer 1

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.