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Differential Calculus

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3 Jul 2009 22:24:33 IST

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let f(x)=x^3+ax^2+bx+5 sin^2x be an increasing function in the set of real numbers R.then a and b sa

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let f(x)=x^3+ax^2+bx+5 sin^2x be an increasing function in the set of real numbers R.then a and b satisfiy the condition(a) a^2-3b-15 &= o(c) a^2-3b+15 0 and b> 0 (A)a^2_3b-

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Bipin Dubey

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Joined: 23 Jan 2007

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4 Jul 2009 23:50:14 IST

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Since f(x) is an increasing function : f '(x) > 0

f '(x) = 3x² + 2ax + b + 10sinx.cosx = 3x² + 2ax + b + 5sin2x > 0

As we know : 5 > 5sin2x

3x² + 2ax + b + 5 > 3x² + 2ax + b + 5sin2x > 0

3x² + 2ax + b + 5 > 0

Its discriminant should be less than 0 : (2a)² - 4(3)(b+5) > 0

a² - 3b - 15 > 0

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