Question #1989

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

Expert's answer

Let's integrate f'':

f' = 2x - 7/2 x^{2 }- 19/2 x^{4} +C_{1}

Since f'(0) = 4 C_{1} = 4

f = x^{2} - 7/6 x^{3} -19/10 x^{5} +4x + C_{2}

f(0) =1 , C_{2} = 1

f(x) = x^{2} - 7/6 x^{3} -19/10 x^{5} +4x + 1.

f' = 2x - 7/2 x

Since f'(0) = 4 C

f = x

f(0) =1 , C

f(x) = x

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