For f(x)=x3+bx2+cx+d, if b24c0 and b,c,d∈ R, then f(x)

Question

For f(x)=x3+bx2+cx+d, if b2>4c>0 and b,c,d∈ R, then f(x) (A) is strictly increasing (B) is strictly decreasing (C) has a local maxima (D) is bounded

Tardigrade Admin · Accepted Answer

f' (x) = 3 x2 + 2 b x + c Discriminant =4(b2 - 3 c)>4c>0 (as c > 0) Hence, f(x) has a local maxima and a local minima

Q. For $f (x) = x^{3} + b x^{2} + c x + d,$ if $b^{2} > 4 c > 0$ and $b, c, d \in R,$ then $f (x)$