Consider the cubic

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the cubic f(x)=8x3+4ax2+2bx+af(x)=8x^3+4ax^2+2bx+a, where a,b∈Ra,b\in\mathbb{R}. For a=1a=1, if y=f(x)y=f(x) is strictly increasing for all x∈Rx\in\mathbb{R}, then the maximum range of values of bb is (1) (−∞,13]\left(-\infty,\dfrac13\right] (2) (13,∞)\left(\dfrac13,\infty\right) (3) [13,∞)\left[\dfrac13,\infty\right) (4) (−∞,∞)(-\infty,\infty)

Related theory

Browse the problem library