The slope of the tangent line of the given graph of f(x) is found by the ratio of the rise to the run of the tangent line at x = -2, which gives;
- The slope of the tangent line at x = -2 is 1/2
How can the slope of a line, tangent to the curve of the graph be found?
The tangent to a curved graph at a point is given by a line that is perpendicular to the radius of the curve at that point.
The formula that gives the tangent is expressed as follows;
- [tex]tan( \theta) = \frac{d f(x)}{dx} = \frac{dy}{dx} [/tex]
Examination of the graph gives;
The slope at the point x = -2 is positive
The maximum slope from x = -6.5 to x = -1.5 is approximately 3/2 = 1.5
Therefore;
The option that gives the estimate for the slope of the tangent line at x = -2 is therefore;
- The slope of the tangent line at x = -2 is 1/2
Learn more about the tangent to a curve here:
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