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Popular >

extreme x+sqrt(1-x)

Solution

extreme points

x + 1 - x

Solution

Maximum (\frac{3}{4}, \frac{5}{4}), Minimum (1, 1)

Solution steps

f^{'} (x) = 1 - \frac{1}{2 1 - x}

Find intervals:

Increasing

: - \infty < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < 1

Plug

x = \frac{3}{4}

into

x + 1 - x : \frac{5}{4}

Maximum (\frac{3}{4}, \frac{5}{4})

Plug

x = 1

into

x + 1 - x : 1

Minimum (1, 1)

Maximum (\frac{3}{4}, \frac{5}{4}), Minimum (1, 1)

Popular Examples

critical 2x^3-2x^2+7x+5 critical points

2 x^{3} - 2 x^{2} + 7 x + 5

range of y=9sqrt(x)+4 range

y = 9 x + 4

line (0,0),(4,5)line

(0, 0), (4, 5)

asymptotes of (8x^2+1)/(4x^3-2x^2+1)asymptotes

\frac{8 x ^{2} + 1}{4 x ^{3} - 2 x ^{2} + 1}

extreme f(x)=(x-2)/(x^2+3x+6)extreme points

f (x) = \frac{x - 2}{x ^{2} + 3 x + 6}

Frequently Asked Questions (FAQ)

What is the extreme x+sqrt(1-x) ?
The extreme x+sqrt(1-x) is Maximum(3/4 , 5/4),Minimum(1,1)