If \(f ' '(x) = 2\), \(f ' (1) = 0\) and \(f(0) = - 8\), find f(x).
Question 1 Report
If \(f ' '(x) = 2\), \(f ' (1) = 0\) and \(f(0) = - 8\), find f(x).
Answer Details
Given \(f''(x)=2,\ f'(1)=0,\ f(0)=-8\), find \(f(x)\).
Integrate \(f''(x)=2\) once:
\[f'(x)=2x+C_1\]Use \(f'(1)=0\):
\[2(1)+C_1=0\;\Rightarrow\;C_1=-2,\qquad f'(x)=2x-2\]Integrate again:
\[f(x)=x^{2}-2x+C_2\]Use \(f(0)=-8\):
\[0-0+C_2=-8\;\Rightarrow\;C_2=-8\]Therefore
\[f(x)=x^{2}-2x-8\]Download The App On Google Playstore
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