For define on the interval

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

For

k\in\mathbb{R}

define

q_k(x)=x^{2}+kx

on the interval

[0,3]

. Determine all real values of

k

for which the average value of

q_k

[0,3]

exceeds the average value of

p(x)=x^{2}

on the same interval.