Let f(x) = x^3 + bx^2 + cx + d where 0

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(D) Given $f(x) = x^3 + bx^2 + cx + d$. Find the derivative: $f'(x) = 3x^2 + 2bx + c$. To determine the nature of the function,check the discriminant

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is strictly increasing

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(D) Given $f(x) = x^3 + bx^2 + cx + d$. Find the derivative: $f'(x) = 3x^2 + 2bx + c$. To determine the nature of the function,check the discriminant $D$ of the quadratic $f'(x)$: $D = (2b)^2 - 4(3)(c) = 4b^2 - 12c = 4(b^2 - 3c)$. Given $0 Since the leading coefficient of $f'(x)$ is $3 > 0$ and $D  0$ for all $x \in \mathbb{R}$. Therefore,$f(x)$ is strictly increasing.

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

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