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(a) y = -3x + 1

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Q: An equation of the line tangent to the graph of y equals x3 plus 3x2 plus 2 at its point of inflection is?

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Yes, the derivative of an equation is the slope of a line tangent to the graph.

A linear equation ?

You find the equation of a graph by finding an equation with a graph.

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Graph and Table: http://i50.tinypic.com/szhr4k.png

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That line is [ y = 2 cos(2x) ].

0.5

Yes, the derivative of an equation is the slope of a line tangent to the graph.

For the equation (9x^2)/(x^2+4)

35

Tangent line is a graph. This graph is to gather data.

The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.

The equation 2x - 3y = 6 is a linear equation and a linear equation is always has a straight line as a graph

To find the inflection points on a graph, you need to take the second derivative. Then, set that equal to zero to find the x value(s) of the inflection point(s).

The equation has no slope. The graph of the equation is a straight line with a slope of -1 .

That's not an equation, so there's nothing to graph. Simple way to tell: There's no "equals" sign in it.

The equation 0 equals 0 is an identity and contributes absolutely nothing to the part of the graph that you should shade or not. The tautological statement can be ignored.

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