Limits, Continuity & Differentiability
General
Grade 12
Question:
<p><span class="math-inline">\(f(x)=4|2x+3|+9[x+\frac{1}{2}]-12[x+20]\)</span>. Non-diff in (-20,20):</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>[x+20]=[x]+20. [x] breaks at integers (39 interior), [x+1/2] breaks at half-integers (39 interior), |2x+3| at x=-3/2 (a half-integer, already counted). Total unique points = 39+39+1=79 but -3/2 is already in half-integers list. So 39+39=78 then check x=-3/2 is included. Total=79. <strong>Answer: 79</strong></p><div class="key-concept"><strong>Key Concept:</strong> Count breakpoints from each piece; half-integers and integers are disjoint sets</div></div>
Correct Answer: 79