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

Aman Nautiyal

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(b) a^2-3b+15 >&= o(c) a^2-3b+15 <&= o(d) a>0 and b> 0 (A)a^2_3b-

Bipin Dubey

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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