Question

Observe the following statements for the curve $y=2.e^{\frac{-x}{3}}$
I : The slope of the tangent to the curve where it meets y-axis is $\frac{-2}{3}$
II:The equation of normal to the curve where it meets y-axis is $3x+2y+4=0$.
Which of the above statement is correct

• A. only I
• B. only II
• C. both I and II
• D. neither I nor II

Answer 1

The correct option is A only I

$y^{\prime }=\frac{-2}{3}{e}^{-x}$
$y^{\prime }{|}_{x=0}=\frac{-2}{3}$
$y=2,x=0$
$(y-2)=\frac{3}{2}(x-0)$
$2y-3x-4=0$
only 2 is true