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Definition
1. Given any x1 & x2 from an interval I with x1 < x2 if f ( x1 ) < f ( x2 ) then f ( x ) is increasing on I.
2. Given any x1 & x2 from an interval I with x1 < x2 if f ( x1 ) > f ( x2 ) then f ( x ) is decreasing on I.
This definition will in fact be utilized in the proof of the next fact in this section.
The Given fact summarizes up what we were doing in the previously
Fact
1. If f ′ ( x ) = 0 for each x on some interval I, then f ( x) is increasing on the interval.
2. If f ′ ( x ) = 0 for each x on some interval I, then f (x ) is decreasing on the interval.
3. If f ′ ( x ) = 0 for each x on some interval I, then f ( x ) is constant on the interval.
Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
how would I graph the equation 2x-5y=5?
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R.2,4,6,8,10 B.8,10
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Find the area enclosed between two concentric circles of radii 3.5cm, 7cm. A third concentric circle is drawn outside the 7cm circle so that the area enclosed between it and the 7
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