Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>g(x)=|f(x)|+f(|x|). In (-2,2), g is:</p>
diff everywhere
not diff 2 pts
not continuous
<strong>not diff 1 pt</strong>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>For x∈(0,2): g=|x²-1|+(x²-1). Non-diff at x=1 where corner. For x∈(-2,0): g=1+(x²-1)=x², smooth. At x=0: continuous and differentiable. So g not diff at exactly 1 point. <strong>Answer: (4) not diff at one point</strong></p><div class="key-concept"><strong>Key Concept:</strong> |f|+f: doubled when f>0, zero when f<0 — corner at zeros of f</div></div>
Correct Answer: 4