Answer: 1.
- A n!
- B 1
- C n
- D 0
Correct answer: B. 1
Explanation: Taylor series: eˣ = Σ(xⁿ/n!). The coefficient of xⁿ is f⁽ⁿ⁾(0)/n!, and here it equals 1/n!. So f⁽ⁿ⁾(0) = 1 for all n ≥ 0, confirmed since d<sup>n</sup>/dx<sup>n</sup>(eˣ) = eˣ and e⁰ = 1.
As point Q slides along the curve toward P, the secant line PQ rotates into the tangent line at P, whose slope is the derivative.
Concept context
Rate of change, differentiation rules, and applications