Question

On [1, e], the greatest value of x²logx is

(A) e²

(B) 1/e(log(1/√e))

(C) e²log√e

(D) None of these

Answer 1

Answer is (A) e²

We have

f(x) = x²logx ⇒ f'(x) = (2logx + 1)x

Now, f'(x) = 0 ⇒ x = e^-1/2, 0

Since 0< e^-1/2 < 1  and none of these critical points lies in the interval [1, e], we only complete the value of f(x) at the end points 1 and e. We have f(1) = 0, f(e) = e². Therefore, the greatest value is e².