Let and . On which of the following intervals are both and increasing…

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

Problem

Let

f(x)=e^{2x}-3x

and

g(x)=x^{3}-6x

. On which of the following intervals are both

f

and

g

increasing simultaneously? (a)

(-\sqrt{2},\sqrt{2})

(b)

(-\infty,-\sqrt{2})\cup(\sqrt{2},\infty)

(c)

(\sqrt{2},\infty)

(d)

\left(\frac{1}{2}\ln\!\left(\frac{3}{2}\right),\,\sqrt{2}\right)