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| Math Central | Quandaries & Queries |
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Graph the function f(X)= x+1/x-1 and graph the tangent line to the function at the points A:(2,3) and B:(-1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC. |
Hi Christina.
To solve this question, I'd start by finding the derivative of f at the two points. Then, using the point-slope form, I'd have the equations of the two tangent lines. Use these two equations in two unknowns to find the point of intersection.
Now with three points, I'd probably proceed to use the distance formula to find the lengths of the three sides of the triangle. Then I'd use Heron's formula for the area of the triangle using the lengths of the sides.
Hope this outline helps you,
Stephen La Rocque.
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