Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Multiplicative functional equation, <span class="math-inline">\(f'(1)=2024\)</span>. ODE:</p>
<strong>xf'(x)-2024f(x)=0</strong>
xf'(x)+2024f(x)=0
xf'(x)+f(x)=2024
xf'(x)-f(x)=2024
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f(x)=x^{2024}. Differentiate: xf'(x)=2024f(x). <strong>Answer: (1) xf'(x)-2024f(x)=0</strong></p><div class="key-concept"><strong>Key Concept:</strong> f(x/y)=f(x)/f(y) ⟹ power function; ODE by differentiation</div></div>
Correct Answer: 1