Question

Check whether the tangents to the curve $y=2x^2-6x$ at the points $(0,0)$ and $(3,0)$ are at right angle or not?

Answer 1

The equation of curve is $y=2x^2-6x$.
Differentiating with respect to $x$ gives slope of the tangent i.e.,
$\frac{dy}{dx}=4x-6$

Let, $m_1$ be the slope of tangent at $(0,0)$ and $m_2$ be the slope of tangent at $(3,0)$
$\therefore m_1=4\left(0\right)-6=-6$ and $m_2=4\left(3\right)-6=6$

Clearly, $m_1{m}_2=-6\times 6=-36\ne -1$
$\therefore$ The tangents of the given curve at $(0,0)$ and $(3,0)$ are not at right angle.