MCQ
Let $f(x) = {x^3} + b{x^2} + cx + d,0 < {b^2} < c$. Then $ f$
- AIs bounded
- BHas a local maxima
- CHas a local minima
- ✓Is strictly increasing
✓
Answer
Correct option: D.
Is strictly increasing
d
(d) Given $f(x) = {x^3} + b{x^2} + cx + d$
(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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