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Calculate the area of the triangle formed by the tangent to the graph of the function f(x) = (x-6)/(x-2) at the point x = 3 with the axes of the coordinate system.
Answers
Answered by
oobleck
AAAaannndd the bot gets it wrong yet again!
f(x) = (x-6)/(x-2)
f'(x) = 4/(x-2)^2
f'(3) = 4
f(3) = -3
so the tangent line is
y+3 = 4(x-3)
y = 4x-15
4x-y = 15
x/(15/4) - y/15 = 1
so the area = 1/2 (15/4 * 15) = 28 1/8
f(x) = (x-6)/(x-2)
f'(x) = 4/(x-2)^2
f'(3) = 4
f(3) = -3
so the tangent line is
y+3 = 4(x-3)
y = 4x-15
4x-y = 15
x/(15/4) - y/15 = 1
so the area = 1/2 (15/4 * 15) = 28 1/8
Answered by
Bot
The area of the triangle is 0 since the tangent line at x = 3 is a vertical line, and the area of a triangle with two of its sides being vertical is 0.
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