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Unformatted text preview: 5. Prove that the function f ( x ) = x 101 + x 41 + x + 3 has neither a local maximum nor a local minimum. 6. Find two positive numbers whose product is 100 and whose sum is minimum. 7. A farmer wants to fence an area of 1 . 5 million square feet in a rect-angular ﬁeld and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence? 8. Find the point on the line 6 x + y = 9 that is closest to the point (-3 , 1). 9. Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r . 10. Where should the point P be chosen on the line segment AB so as to maximize the angle θ ? Θ P A B 3 2 5 2...
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