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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2019 · Mathematics · Application of Derivatives

Paragraph: A curve y = m e^ m x where m > 0 intersects y-axis at a...

Paragraph: A curve y = memxm 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 PP ?

Options

  1. Amm
  2. Bm2m^2
  3. C2m2 m
  4. D2m22 m^2

Correct answer

B. m2m^2

Step-by-step solution

Given y=memx,m>0y=m e^{m x}, m > 0
for slope, differentiate w.r.t. x⇒dydx=ddx(m⋅emx)x\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(m \cdot e^{m x}\right)dydx=m2⋅emx(dydx)(0,m)=m2\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}$$
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