The equation of the tangent to the curve `y=4xe^(x)` at `(-1,(-4)/e)` is

Options

A. `y=-1`
B. `y=-4/e`
C. `x=-1`
D. `x=(-4)/e`

Answer

B

Explanation

Given curve is `y=4xe^(x)`
`implies(dy)/(dx)=4d^(x)+4xe^(x)`
At `(-1,-4/e),((dy)/(dx))_((-1,-4/e))=4e^(-1)+4(-1)e^(-1)=0`
`:.` Equation of tangent is
`(y+4/e)=0(x+1)impliesy=-4/e`