For the function

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For the function

f(x)=x^{3}+kx^{2}+x+1

, determine all real values of

k

for which

f

is strictly increasing on

\mathbb R

. (a)

|k|\le \sqrt{3}

(b)

|k|>\sqrt{3}

(c)

|k|<\sqrt{3}

(d)

|k|<\dfrac{\sqrt{3}}{2}