Question

If a tangent to the curve$y=6x–x^2$ is parallel to the line$4x–2y–1=0$, then the point of tangency on the curve is

• A. $(2,8)$
• B. $(8,2)$
• C. $(6,1)$
• D. $(4,2)$

Answer 1

The correct option is A

$(2,8)$

Find the point of tangency:

Given the curve $y=6x–x^2$

$\Rightarrow \frac{dy}{dx}=6–2x$

The tangent is parallel to the line $4x–2y–1=0$

$$\begin{gathered} \Rightarrow 4-2\frac{dy}{dx}=0 \\ \Rightarrow \frac{dy}{dx}=\frac{4}{2} \\ \Rightarrow 6–2x=\frac{4}{2} \\ \Rightarrow 6–2x=2 \\ \Rightarrow x=2 \end{gathered}$$

and $y=8$

The required point of tangency will be $(2,8)$.

Hence, the correct option is A.