Question

Statement-1: The line $\frac{x}{a}+\frac{y}{b}=1$ touches the curve $y=b{e}^{-\frac{x}{a}}$ at some point $x=x_0$.
Statement-2: $\frac{dy}{dx}$ exists at $x=x_0$.

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is true.

Answer 1

Answer: (B)

Line touches the curve at $(0,b)$ and ${\frac{dy}{dx}]}_{x=0}$ also exists but even if $\frac{dy}{dx}$ fails to exist. tangents line can be drawn.