Exercise · ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-010 · ★★★ Advanced
It is known that \(\mathcal L\{f''\}=s^2F(s)-2s+3\). What are \(f(0)\) and \(f'(0)\)?
Choose one option.
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- A. \(f(0)=2,\ f'(0)=-3\)
Explanation
Comparing with \(s^2F-sf(0)-f'(0)\): \(sf(0)=2s\) gives \(f(0)=2\), and \(-f'(0)=3\) gives \(f'(0)=-3\).
Review the concept: Laplace transform of a derivative
The Laplace transform \(\mathcal L\) of the derivative \(f'\) of a function \(f(t)\) with transform \(F(s)\) is an expression in \(F(s)\) and the initial value \(f(0)\).
\[\mathcal L\{f'\}(s)=sF(s)-f(0)\]
More practice problems: laplace transform of a derivative
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