Mathematics - Application of Derivative Question with Solution | TestHub

Let $P\left(x_1,y_1\right)$ be a point on the curve $y=x^2+3x+4$ $\begin{array}{rlr}& \Rightarrow y_1=x_1^2+3x_1+4& {\left(\frac{dy}{dx}\right)}_{at\left(x_1,y_1\right)}=2x_1+3\end{array}$

Equation of tangent is: $y-y_1=m\left(x-x_1\right)$. It passes through $(0,0)$ Then $y_1=2x_1^2+3x_1$ From (1) and (2) $x_1=\pm 2$ ∴ the points are $(2,14)$ and (-2, 2)