If f(x) = x³ - 2x + 5, find f'(1).

**The reasoning** To find f'(1), we need to differentiate f(x) first, then substitute x = 1. Using the **power rule of differentiation**: if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹ Given f(x) = x³ - 2x + 5 Differentiating term by term: - x³ becomes 3x² - -2x becomes -2 (since x¹ becomes 1x⁰ = 1) - 5 becomes 0 (constants vanish when differentiated) So f'(x) = 3x² - 2 Now substitute x = 1: f'(1) = 3(1)² - 2 = 3(1) - 2 = 3 - 2 = **1** **Why the wrong options tempt you** **A) 0** — You might get this if you forgot to subtract 2, or mixed up f'(1) with finding where f'(x) = 0. **C) 2** — This comes from forgetting the "-2" entirely, giving just 3(1)² - 1 = 2. **D) 4** — You probably substituted into the original function f(1) = 1 - 2 + 5 = 4, instead of the derivative. **Quick takeaway** Differentiate *first* using the power rule, *then* substitute the value — never reverse the order!