Application of Derivatives
Tangents and Normals
IIT-JEE 2003
Grade 12
Question:
The tangent to the curve $y = e^{2x}$ at the point $(0, 1)$ meets the $x$-axis at:
(1) $\left(-\frac{1}{2}, 0\right)$
(2) $\left(\frac{1}{2}, 0\right)$
(3) $(-2, 0)$
(4) $(2, 0)$
Step-by-Step Solution
Key Concept: Differentiate $y = e^{2x}$ to find the slope of the tangent at $x = 0$, then write down the equation of the tangent line through $(0, 1)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)