For defined on

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

Problem

For

g(x)=x^{3}+k x^{2}

defined on

[1,4]

, determine the condition on

k

so that

g

is strictly decreasing throughout

[1,4]

. (a)

k=-6

(b)

k<-6

(c)

-6<k< -\dfrac{3}{2}

(d)

k< -\dfrac{3}{2}