Question

If a tangent to the curve$y=2+\sqrt{4x+1}$ has slope $2/5$ at a point, then the point is

• A. $(0,2)$
• B. $(3/4,4)$
• C. $(2,5)$
• D. $(7,6)$
• E. $(6,7)$

Answer 1

The correct option is E

$(6,7)$

Finding the point :

Given curve $y=2+\sqrt{4x+1}$ has slope $2/5$.

$$\begin{gathered} \Rightarrow \frac{dy}{dx}=\frac{1}{2\sqrt{(4x+1)}}\times 4 \\ \Rightarrow \frac{dy}{dx}=\frac{2}{\sqrt{(4x+1)}} \\ \Rightarrow \frac{2}{5}=\frac{2}{\sqrt{(4x+1)}} \\ \Rightarrow 4x+1=25 \\ \Rightarrow x=6 \end{gathered}$$

Put $x=6$in the given curve

$$\begin{gathered} \Rightarrow y=2+\sqrt{25} \\ \Rightarrow y=2+5 \\ \Rightarrow y=7 \end{gathered}$$

Thus required point is $(6,7)$

Hence, the correct option is E.