Ques. -27

Calculus Level 3

If f ( x ) = x 3 + b x 2 + c x + d f(x)=x^3+bx^2+cx+d and 0 < b 2 < c 0<b^2<c , then in ( − ∞ , ∞ ) (-\infty, \infty) :

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f(x) has a local maxima. f(x) is strictly increasing function. f(x) is bounded. f(x) is strictly decreasing function.

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Rohit Ner
Sep 9, 2015

f ′ ( x ) = 3 x 2 + 2 b x + c D = 4 b 2 − 12 c b 2 < c → 4 b 2 < 12 c → D < 0 ∀ x ∈ R f ′ ( x ) > 0 ∀ x ∈ R f'(x)=3{x}^2+2bx+c\\D=4{b}^2-12c\\{b}^2<c\\\rightarrow 4{b}^2<12c\\\rightarrow D<0 \forall x \in\mathbb R\\ f'(x)>0 \forall x\in \mathbb R .
Hence, f ( x ) f(x) is strictly increasing.

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Thushar Mn
Mar 1, 2015

Only condition given for f(x) is b^(2)<c ,So choose b=1,c=2 and d=1.then we can see f(x)is strictly incresing.

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