Find \(\log_e f(4)\) .

x=y=0: f'(0)=1/2. Differentiate: f''=f'/2. So f'=Ce^{x/2}, f'(0)=1/2⟹C=1/2. f=e^{x/2}. log_e f(4)=2. Answer: 2 Key Concept: Derive ODE from functional equation via differentiation

Limits, Continuity & Differentiability

General

Grade 12

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<div class="solution"><p>x=y=0: f'(0)=1/2. Differentiate: f''=f'/2. So f'=Ce^{x/2}, f'(0)=1/2⟹C=1/2. f=e^{x/2}. log_e f(4)=2. <strong>Answer: 2</strong></p><div class="key-concept"><strong>Key Concept:</strong> Derive ODE from functional equation via differentiation</div></div>

Correct Answer: 2

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