Limits, Continuity & Differentiability
General
Grade 12
Question:
<p><span class="math-inline">\(f(x)=|x^2-2x-3|\cdot e^{|9x^2-12x+4|}\)</span> non-diff at:</p>
4 points
3 points
<strong>2 points</strong>
1 point
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>|x²-2x-3|=|(x-3)(x+1)|: corners at x=-1,3. |(3x-2)²|=(3x-2)² always ≥0, absolute value redundant. Non-diff at x=-1,3 → 2 points. <strong>Answer: (3) two points</strong></p><div class="key-concept"><strong>Key Concept:</strong> e^{u} is differentiable; non-diff only from |polynomial| zeros</div></div>
Correct Answer: 3