If f(x)=x^3+b x^2+c x+d and 0

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(B) Given $f(x) = x^3 + bx^2 + cx + d$. Taking the derivative with respect to $x$,we get $f'(x) = 3x^2 + 2bx + c$. For $f(x)$ to be strictly increasin

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$f(x)$ is strictly increasing function.

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(B) Given $f(x) = x^3 + bx^2 + cx + d$. Taking the derivative with respect to $x$,we get $f'(x) = 3x^2 + 2bx + c$. For $f(x)$ to be strictly increasing,we need $f'(x) > 0$ for all $x \in \mathbb{R}$. The quadratic expression $3x^2 + 2bx + c$ is always positive if its discriminant $D Here,$D = (2b)^2 - 4(3)(c) = 4b^2 - 12c = 4(b^2 - 3c)$. Since $0  0$). More directly,since $b^2 Thus,$D  0$ for all $x \in \mathbb{R}$. Therefore,$f(x)$ is a strictly increasing function.

If $f(x)=x^3+b x^2+c x+d$ and $0 < b^2 < c$,then in $(-\infty, \infty)$

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