Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 35

False; $\frac{d}{dx}(4f(x) + x^3) |_{x=2} \neq 20$.

The error in this example occurs when the writer evaluates $x^3$ at $x=2$ before differentiating. Correct answer: If $f'(2) = 5$, then \begin{align} & \frac{d}{dx}(4f(x) + x^3) |_{x=2} \\ &= 4f'(x) + 3x^2 |_{x=2} \\ &= 4f'(2) + 3(4) \\ &= 4(5) + 12 \\ &= 32 \\ \end{align}