Question

A curve $y=m{e}^{mx}$ where $m>0$ intersects y-axis at a point $P$.

What is the equation of tangent to the curve at $P$ ?

• A. $y=mx+m$
• B. $y=-mx+2m$
• C. $y=m^{2}x+2m$
• D. $y=m^{2}x+m$

Answer 1

Answer: (D)

$y=m^{2}x+m$

$y=m{e}^{mx},m>0$

Substituting $x=0$, we have

$y=m{e}^{m\cdot 0}=m$

Therefore,

Slope $=\frac{dy}{dx}=m^2{e}^{mx}=m^2{e}^{m\cdot 0}=m^2$

Therefore, equation of tangent at $P$ is given by-

$y-m=\frac{dy}{dx}(x-0)$

$\Rightarrow y-m=m^{2}x$

$\Rightarrow y=m^{2}x+m$