If 0

Question

If 0 < x ≤ 1, then which one of the following is the maximum value of (x – 1)^2 + x ?

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2

Bunuel · Accepted Answer

If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 1 is when x=1 --> (x – 1)^2 + x = 1 you can do the following: Since 0 < x ≤ 1, then (x – 1)^2 + x is positive --> discard A, B and C. For the same reason: (x – 1)^2 is a non-negative fraction less than 1. Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 1) < 2. Discard E. Only D is left. Answer: D.

mau5 · Answer

As x is a positive entity, the sum of the given expression can never be negative or zero.Eliminate all except D and E.

There are many ways to ascertain the maximum value now.

For example,
The given expression results as x^2-x+1 	o x(x-1)+1

For x=1, we have the sum as 1

For 0< x<1, we have the expression as : 1-(a negative quantity)

Thus, maximum value is for x=1.

D.

vad3tha · Answer

I like the way you discard E. Thanks. +1 kudos

PareshGmat · Answer

Given that 0 < x ≤ 1

Placing value of x = 1 in the above equation:

(1-1)^2 + 1 = 1

Answer = D

philipssonicare · Answer

We get the same result when x=0  (0-1)^2+0=1

The small range provided made it easy to try subbing in 0, 0.5, and 1, but a larger range would be difficult. How are we meant to approach when a range is larger?

bumpbot · Answer

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If 0 < x ≤ 1, then which one of the following is the maximum

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