At what point does the tangent to the curve y = eˣ intersect the y-axis if the tangent is drawn at the point (0, 1)?

At what point does the tangent to the curve y = eˣ intersect the y-axis if the tangent is drawn at the point (0, 1)?

• A. (0, 1)
• B. (1, 0)
• C. (0, 0)
• D. (0, e)

Answer: A) (0, 1)

Explanation: y = eˣ implies dy/dx = eˣ. At (0, 1), m = e⁰ = 1. Equation of tangent is y - 1 = 1(x - 0), which is y = x + 1. The y-intercept is at x = 0, giving y = 1. Point is (0, 1).