The given equation is,
[tex]p(x)=3x^2+6x\text{ ---(1)}[/tex]
Differentiate the above equation.
[tex]\begin{gathered} \frac{dp(x)}{dx}=3\times2x+6 \\ \frac{dp(x)}{dx}=6x+6\text{ ---(2)} \end{gathered}[/tex]
dp(x)/dx is the slope of the tangent to curve p(x).
The given point is (x, y)=(-1, 5).
Take x=-1 and put it in equation (1).
[tex]\begin{gathered} y=p(x)=3\times(-1)^2+6\times(-1) \\ =3-6 \\ =-3 \end{gathered}[/tex]
So, the y coordinate is not 5. Hence, there is no tangent to p(x) that passes through point (-1, 5)
