Let f(x) = x^3 + b x^2 + cx + d,0 < b^2 < c. Then f - Vidyadip

MCQ

Let $f(x) = {x^3} + b{x^2} + cx + d,0 < {b^2} < c$. Then $ f$

A
Is bounded
B
Has a local maxima
C
Has a local minima
✓
Is strictly increasing

✓

Answer

Correct option: D.

Is strictly increasing

d
(d) Given $f(x) = {x^3} + b{x^2} + cx + d$

$\therefore$ $f'(x) = 3{x^2} + 2bx + c$

Now its discriminant $ = 4({b^2} - 3c)$

==> $4({b^2} - c) - 8c < 0,$ as ${b^2} < c$ and $c > 0$

Therefore, $f'(x) > 0$ for all $x \in R$

Hence $ f$ is strictly increasing.

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