Limits, Continuity & Differentiability
General
Grade 12
Question:
<p><span class="math-inline">\(f(x+y)=f(x)+f(y)+xy^2+x^2y\)</span>, <span class="math-inline">\(\lim_{x\to 0}f(x)/x=1\)</span>. Find <span class="math-inline">\(f'(3)\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f'(0)=1. Differentiate w.r.t. x, set x=0: f'(y)=1+y². f'(3)=10. <strong>Answer: 10</strong></p><div class="key-concept"><strong>Key Concept:</strong> Differentiate functional equation then set x=0</div></div>
Correct Answer: 10