Paragraph: A curve y = $m e^{m x}$ where m > 0 intersects y-axis at a point P.
Question: What is the slope of the curve at the point of intersection $P$ ?

• A

  $m$
• Correct answer
  B

  $m^2$
• C

  $2 m$
• D

  $2 m^2$

Solution

Given $y=m e^{m x}, m \gt 0$
for slope, differentiate w.r.t. $x$ $\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(m \cdot e^{m x}\right)$ $\begin{aligned} & \frac{d y}{d x}=m^2 \cdot e^{m x} \\ & \left(\frac{d y}{d x}\right)_{(0, m)}=m^2\end{aligned}$

Hence, the correct answer is option: 'B'.