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Solve for m. Solve for the point on the graph for x=-1. Solve for equation of the tangent at x=-1.

Solve for m. Solve for the point on the graph for x=-1. Solve for equation of the-example-1
User Joel Nieman
by
2.5k points

1 Answer

16 votes
16 votes

First, let's calculate the derivative of y:


\begin{gathered} y=2x^2+3x-4\\ \\ (dy)/(dx)=2\cdot2x+3\operatorname{\cdot}1-0\\ \\ (dy)/(dx)=4x+3 \end{gathered}

Now, for x = -1, we have:


4x+3=4\operatorname{\cdot}(-1)+3=-4+3=-1

So the slope of the tangent line when x = -1 is equal to m = -1.

Let's calculate the value of y when x = -1:


\begin{gathered} y=2\operatorname{\cdot}(-1)^2+3\operatorname{\cdot}(-1)-4\\ \\ y=2-3-4=-5 \end{gathered}

So the point on the graph for x = -1 is (-1, 5)

User Moritzpflaum
by
3.1k points
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