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14 votes
14 votes
is my answer correct? question : prove that there is no tangent line to
p(x) = 3x^(2) + 6xthat passes through the point (-1;5)

is my answer correct? question : prove that there is no tangent line to p(x) = 3x-example-1
User Yuriy Zhigulskiy
by
3.4k points

1 Answer

21 votes
21 votes

The equation is given by:


\begin{gathered} p(x)=3x^2+6x \\ p^(\prime)(x)=6x+6 \end{gathered}

Slope of tangent will be:


p^(\prime)(-1,5)=m=6(-1)+6=0

The equation of tangent is given by:


\begin{gathered} y-5=0(x-(-1)) \\ y=5 \end{gathered}

The line is tangent if it touches the curve at a single point:

Substitute P(x)=5 to get:


\begin{gathered} 3x^2+6x=5 \\ 3x^2+6x-5=0 \end{gathered}

The line is tangent if the discriminant is 0 so it follows:


\Delta=6^2-4(3)(-5)=96>0

Hence the roots of the equation are real and unequal.

Hence there is no tangent that can be drawn from point (-1,5) to the given curve.

User Vijay Sebastian
by
3.2k points