Quote:
Originally posted by BreakABone
A tangent line drawn to the parabola y=4-x2 at the pont (1,3) forms a right triangle with the coordinate axes. The area of the triangle is....
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Edit: stupid signs switching on me...ok, here's my second try.
If you take the derivative of the parabola's function, you get dy/dx = -2x. You know that the line intersects at the point (1,3). In other words, where x = 1. Plugging that into the derivative function of the parabola, you get dy/dx = -2.
So now you know the slope of the line is -2 and it passes through the point (1,3). You know how to come up with the equation fo the line from here (I presume). If you want to do this on your own from here, don't read any further. Just check back here to verify your answer.
Are you gone yet? Ok, here goes.
The equation you should get is y = -2x + 5. So you know that the x-intercept is 5/2 and the y-intercept is 5. If you draw everything out on graph paper, you'll see that the base and height of the triangle are 1/2 unit long and 1 unit long respectively. So using the area of a triangle formula, you find that the area of the triangle is 5/2 x 5 x 1/2 or 25/4.