Question

The equation of the tangent to the curve $y=4x{e}^x$ at $(-1,\frac{-4}{e})$ is

• A. $y=-1$
• B. $y=-\frac{4}{e}$
• C. $x=-1$
• D. $x=\frac{-4}{e}$

Answer 1

The correct option is B $y=-\frac{4}{e}$

Given curve is $y=4x{e}^x$
$\frac{dy}{dx}=4e^x+4x{e}^x$
At $(-1,-\frac{4}{e}){\left(\frac{dy}{dx}\right)}_{(-1,-4/e)}=4e^{-1}+4(-1)e^{-1}$
$\therefore$ Equation of tangent is $(y+\frac{4}{e})=0(x+1)$
$\Rightarrow y=-\frac{4}{e}$