Limits, Continuity & Differentiability
General
Grade 12
Question:
<p><span class="math-inline">\(f=\min\{1,1+x\sin x\}\)</span> on <span class="math-inline">\([0,2\pi]\)</span>. <span class="math-inline">\((m,n)=\)</span></p>
(2,0)
<strong>(1,0)</strong>
(1,1)
(2,1)
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f=1 when x sin x≤0 (i.e., x∈{0}∪[π,2π]). f=1+x sin x when x∈(0,π). Non-diff at x=π (slope jump). n=0, m=1. Answer: (m,n)=(1,0). <strong>Answer: (2)</strong></p><div class="key-concept"><strong>Key Concept:</strong> min{const,f}: non-diff where f meets constant with non-zero slope</div></div>
Correct Answer: 2