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I m having problem in these two questions: 1) f(x)=x^3+6x^2+(9+2k)x+1 is increasing if k is 2)f(x)=cosx-2PX is monotonically decreasing for p:

I m having problem in these two questions:
 
1) f(x)=x^3+6x^2+(9+2k)x+1 is increasing if k is
 
2)f(x)=cosx-2PX is monotonically decreasing for p:

Grade:12

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
HInt: 1. If we diffirenciate a cubic equation, we get the quadratic equation. Not for cubic polynomial to be increasing function, its derivative should be positive, i.e. quadratic polynomial obtained should be postivie for entire range. Which is posibile if a > 0 and b2 – 4ac < 0 for ax2 + bx + c. Therefore k > 3/2.

2. for f(x) to be decreasing funciton, its derivate should be negative. Use this condition to solve the question. (P > 1/2). Thanks,,

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