Let and on , where is a positive real constant. For which values of is the average…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

f_k(x)=k x

and

g(x)=x^{2}

[0,2]

, where

k

is a positive real constant. For which values of

k

is the average value of

f_k

[0,2]

greater than the average value of

g

on the same interval? (a)

k>\dfrac{2}{3}

(b)

k>2

(c)

k>\dfrac{4}{3}

(d)

0<k<\dfrac{4}{3}