Question Detail
Question
Given the function y = eˣ, find f(x+h) - f(x).
Correct Answer
Option B is the correct answer.
Detailed Explanation
The function is f(x) = eˣ.So, f(x+h) = e⁽ˣ⁺ʰ⁾.Now, calculate f(x+h) - f(x):e⁽ˣ⁺ʰ⁾ - eˣUsing the exponent rule a⁽ᵇ⁺ᶜ⁾ = aᵇ * aᶜ, we have e⁽ˣ⁺ʰ⁾ = eˣ * eʰ.So, eˣ * eʰ - eˣFactor out eˣ:eˣ(eʰ - 1).
Hint
Apply the properties of exponents, specifically e⁽ᵃ⁺ᵇ⁾ = eᵃ * eᵇ, and then factor out common terms.