The condition that $f (x) = x^{3} + a x^{2} + b x + c$ is an increasing function for all values of $^{'} x^{'}$ is

a^{2} < 12 b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a^{2} < 3 b

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a^{3} < 4 b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a^{2} < 16 b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $a^{2} < 3 b$
$f^{'} (x) = 3 x^{2} + 2 a x + b$
$f^{'} (x) > 0$
$3 x^{2} + 2 a x + b > 0$
Determinant $< 0$
$(2 a)^{2} - 4 \times (3 b) < 0$
$a^{2} < 3 b$ .

Suggest Corrections

Similar questions

f (x) = x^{3} + a x^{2} + b x + c, a^{2} \leq 3 b

f (x) = x^{3} + a x^{2} + b x + c i s a n

x

The function $f (x) = x^{3} + a x^{2} + b x + c, a^{2} \leq 3 b$ has

f (x) = \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}

Join BYJU'S Learning Program