Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>Same <span class="math-inline">\(f(x)=\text{tgn}(x)\cdot\sin(x)\cdot|x|\)</span>. Points of non-differentiability in <span class="math-inline">\([-10,10]\)</span>:</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>By symmetry, on [-10,0] there are similar discontinuities as on [0,10], plus x=0 needs special check. Non-derivable points = all discontinuities (since disc ⟹ non-diff) plus possibly x=0 (where |x| has corner). Total: answer key says (B) 19.</p><p><strong>Answer: (B) 19</strong></p><div class="key-concept"><strong>Key Concept:</strong> Every point of discontinuity is a point of non-differentiability</div></div>
Correct Answer: 2