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Popular >

range of x-x^2

Solution

range

x - x^{2}

Solution

f (x) \leq \frac{1}{4}

+1

Interval Notation

(- \infty, \frac{1}{4}]

Solution steps

Vertex of

x - x^{2} :

Maximum

(\frac{1}{2}, \frac{1}{4})

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = - 1,

Vertex

(x_{v}, y_{v}) = (\frac{1}{2}, \frac{1}{4})

f (x) \leq \frac{1}{4}

Popular Examples

extreme f(x)=4x^3-18x^2+24x extreme points

f (x) = 4 x^{3} - 18 x^{2} + 24 x

critical f(x)= 1/(x^2+10x+28)critical points

f (x) = \frac{1}{x ^{2} + 10 x + 28}

asymptotes of f(x)=(-x^2-2x+4)/(x+3)asymptotes

f (x) = \frac{- x ^{2} - 2 x + 4}{x + 3}

inverse of 8x+3 inverse

8 x + 3

range of sqrt(-x)+2 range

- x + 2

Frequently Asked Questions (FAQ)

What is the range of x-x^2 ?
The range of x-x^2 is f(x)<= 1/4