Limits, Continuity & Differentiability
Properties of Derivatives
Grade 12
Question:
<p><strong>Ex. 66</strong> The function \(f'(x)\) is</p>
<p>(a) even function</p>
<p>(b) odd function</p>
<p>(c) neither even nor odd</p>
<p>(d) indefinite</p>
Step-by-Step Solution
Key Concept: A function is even if its graph is symmetric about the y-axis; this means $f'(-x) = f'(x)$.
<p>The graph of $y = f'(x)$ is symmetrical about the Y-axis, so $f'(x)$ is an even function.</p>
Correct Answer: a