Maxed out

Algebra Level 2

Let f ( x ) = ∣ x ∣ × ∣ x − 1 ∣ f(x) = |x| \times |x-1|

What is the maximum value of f ( x ) f(x) over the range 0 < x < 1 0 < x < 1 ?

Notation : ∣ ⋅ ∣ | \cdot | denotes the absolute value function .


The answer is 0.25.

Denton Young by Denton Young , 47, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Denton Young
Jul 26, 2016

In that range, the function is equivalent to x × ( 1 − x ) x \times (1-x)

This has a maximum where x = 1 − x = 0.5 x = 1-x = 0.5

The maximum value is thus 0.5 × 0.5 0.5 \times 0.5 = 0.25 0.25

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...