Question

Consider the curve represented parametrically by the equation
$x=t^3-4t^2-3t$ and $y=2t^2+3t-5$ where $tϵR$.
If $H$ denotes the number of point on the curve where the tangent is horizontal and $V$ the number of point where the tangent is vertical then

• A. $H=2$ and $V=1$
• B. $H=1$ and $V=2$
• C. $H=2$ and $V=2$
• D. $H=1$ and $V=1$

Answer 1

The correct option is B $H=1$ and $V=2$

$\frac{dx}{dt}=3t^2-8t-3$
$\frac{dy}{dt}=4t+3$
$\Rightarrow \frac{dy}{dt}=\frac{4t+3}{3t^2-8t-3}$
clerarly denominator has two roots and numerator has single root
Hence given curve will have two vertical tangent and one horizontal tangent
$\Rightarrow H=1,V=2$