If f x - x 3- px 2- q x -6- p - q - - R - f - x -0 for largest possible interval -5-3-1- then p 2- q 2-A- 41B- 141C- 27D- 37

The correct option is A 41 f'(x)=3x^2+2px+q lt; 0, x ∈[ 5/3, 1 ] ∴ 3x^2+2px+q=(x+1)(3x+5) ∴ p=4, q=5 ⇒ p^2+q^2=4^2+5^2=16+25=41 ...

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AM,GM,HM Inequality

If f x = x 3+...

Question

If $f (x) = x^{3} + p x^{2} + q x + 6, p, q, ϵ R, f^{'} (x) < 0$ for largest possible interval $[- \frac{5}{3}, - 1]$ , then $p^{2} + q^{2} =$

141

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