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A triangle has two vertices fixed at P(a,0) and Q(0,b), while the third vertex R(x,y) moves on the line y = x. If the area of the triangle is A, then the value of dA/dx is

1. (a − b)/2
2. (a − b)/4
3. −(a + b)/2
4. (a + b)/4

Correct answer: −(a + b)/2

Solution

With P(a,0), Q(0,b), R(x,x), area = (1/2)(ab - ax - bx). Differentiating with respect to x gives dA/dx = -(a+b)/2.

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