Question

The slope of tangent to the curve $y=(x-1)e^x$ at point, where curve intersects the $x-$ axis, is

• A. $e-1$
• B. $e$
• C. $e+1$
• D. $2e$

Answer 1

The correct option is B $e$

Given : $y=(x-1)e^x$
For $y=0\Rightarrow x=1$ $(\because e^x\ne 0)$
Differentiating both sides w.r.t. $x$
$\Rightarrow \frac{dy}{dx}=x{e}^x$
Now, the slope of tangent
$\frac{dy}{dx}{|}_{(1,0)}=1\cdot e^1=e$
$\therefore$ slope of tangent is equal to $e$.