Question

antiderivative.
Given f'''(x)=e^x with f''(0)=6, f'(0)=5,
then f(x)=______+C

Answer 1

Integrate, sub for the constant, repeat....

Answer 2

\[\int e^xdx =e^x+C\]
\[f''(x)=e^x+C\] and
\[f''(0)=e^0+C=6\]
\[1+C=6\]
\[C=5\] so
\[f''(x)=e^x+5\]
\[f'(x)=\int e^x+5 dx = e^x+5x+C\]

Answer 3

\[f'(0)=5=e^0+5\times 0+C=1+C\]
\[C=4\] so
\[f'(x)=e^x+5x+4\]

Answer 4

one more time and you get your answer