Discussion Forum



1)

If f(x) = $x^{3}+bx^{2}+cx+d$ and 0<b2<c, then in (-∞, ∞)


A) f(x) is a strictly increasing function

B) f(x) has local maxima

C) f(x) is a strictly decreasing function

D) f(x) is bounded

Answer:

Option A

Explanation:

f(x) = $x^{3}+bx^{2}+cx+d$ and 0<b2<c

.'. f'(x) = $3x^{2}+2bx+c$ 

Discriminant  = 4b2 -12c = 4(b2 - 3c)<0

f'(x) >0 $\forall$ xΕ R

Thus,f(x) is strictly increasing $\forall$ x Ε R