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1. In the coordinate plane, a line passes through the point (12, 3). Its x-intercept is A=(a, 0) where a>0 and its y-intercept is B=(0,b) whre b>0. Find the smallest possible area of triangle OAB, where O is the orgin

2. All the roots of the cubic polynomial f(x)-3x^3+bx^2+cx+d are negative real numbers. If f(0)=81, find the smallest possible value of f(1). Prove that your answer is the minimum

 May 27, 2021
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1. The smallest possible area of triangle OAB is 60.

 

2. The minimum value of f(1) is 144.

 Jun 24, 2021

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