Consider the function f(x) = x - x^2 on the interval (0,1). Which of the following statements is true?
a. f is increasing
b. f is decreasing
c. f is constant
d. f is neither increasing, nor decreasing, nor constant

Question

Consider the function f(x) = x - x^2 on the interval (0,1). Which of the following statements is true?
a. f is increasing
b. f is decreasing
c. f is constant
d. f is neither increasing, nor decreasing, nor constant

anonymous · Answer

at the risk of repeating myself, if you find the vertex you will see that the $x$ coordinate is  $\frac{1}{2}$ which is smack dab in the middle of your interval

anonymous · Answer

I think the answers to choose from are a bit dubious...

anonymous · Answer

So is it constant?

anonymous · Answer

no it is a quadratic polynomial, so it is never constant

anonymous · Answer

So if it is in the middle of the interval it would be D?

anonymous · Answer

yes, increases on $(-\infty, \frac{1}{2})$ and decreases on $(\frac{1}{2}, \infty)$

anonymous · Answer

Ok! I get it now. Thank you :D

anonymous · Answer

yw

anonymous · Answer

So D is also not really true right? :) They probably meant "None of the above statements is true"

anonymous · Answer

Yeah whatever gets me the credit lol