The monotone decreasing interval of the function y = (1 / 2) ^ (x ^ 2 + X + 2) is

Let g (x) = x ^ 2 + X + 2 = (x + 1 / 2) ^ 2 + 7 / 4
Because the base is 1 / 2, the monotone decreasing interval is: x > = - 1 / 2

The monotone decreasing interval of the function y = 2 / X is?

Drawing -- you'll see. Do you want to ask?
The answer is the first and third interval
Or (negative infinity ~ 0) and (0 ~ positive infinity)
In any case, it's the whole range, minus 0

Function y = 1 A monotone interval () A. （-∞，0）∪（0，+∞） B. R C. [0，+∞） D. （-∞，0），（0，+∞）

Function y = 1
The definition domain of X is (- ∞, 0) ∪ (0, + ∞),
From the properties of the inverse proportional function, we can get that,
F (x) decreases on (- ∞, 0) and decreases on (0, + ∞)
Therefore, D

Finding monotone interval of function y = - 1 / x + 1

First find the definition domain, that is, X ≠ 0. This is also an inverse proportional function, so it is monotonically decreasing on x > 0 and increasing monotonically on x < 0. But because there is a "- before 1 / x, it is the opposite, that is, x > 0 increases and X < 0 decreases

The monotone interval of the function y = x + (1 / x) is?

A:
y=x+1/x
y'(x)=1-1/x^2
By solving y '(x) = 1-1 / x ^ 2 = 0, we get: X1 = - 1, x = 1
When x 1, y '(x) > 0, y is a monotone increasing function
-1

The monotone interval of the function y = 1 △ (x + 1) is

(- ∞, - 1) and (- 1, + ∞) are decreasing

This paper discusses the monotone interval and extremum of the function f (x) = x cubic-6x-15x + 2, and finds the concave convex interval and inflection point

Let f '(x) = 3x ^ 2-12x-15 = 0
X1 = - 1, X2 = 5
X belongs to (- infinity, - 1), (5, + infinity), f '(x) > 0, is the monotone increasing interval of F (x);
X belongs to (- 1,5) f '(x) < 0, which is the monotone decreasing interval of F (x)
Let f '' (x) = 6x-12 = 0, x = 2
X belongs to (- infinite, 2) f '' (x) < 0, f (x) is convex function;
X belongs to (2, + infinite) f '' (x) > 0, f (x) is concave function;
When x = 2, the inflection point is (2, - 44)

The monotone interval, extremum, concave convex interval and inflection point of the function y = Xe of x power are obtained in the list

Y '= e ^ x (1 + x), because e ^ x is always greater than 0, we can get x = - 1 from y' = 0
Therefore, the interval of increasing function (- 1, INF)
When x = - 1, y '= 0, the minimum value - 1 / E can be obtained
Y '' = e ^ x (2 + x), when x0, so on the interval (- 2, INF), the function is concave
On both sides of x = - 2, y '' changes sign, so the inflection point is (- 2, - 2 / e ^ 2)

Find monotone interval, concave convex interval, extremum and inflection point of square-12x + 1 of cubic-3x of function y = 2x

y=2x^3-3x^2-12x+1
The derivation of X on both sides of the equation gives y '= 6x ^ 2-6x-12
Let y '= 0 = 6 (x + 1) (X-2) get two extreme points: X1 = - 1, X2 = 2
When X2, y '> 0, the function y increases
When-1

Given the function f (x) = (1 + x) ^ 2-ln (1 + x) ^ 2 (1), find the monotone interval of function f (x) (2) if the function f (x) and the function g (x) = x ^ 2 + X + a are in the interval [0,2] I'm sorry, I forgot to check the number of words in the second question, (2) If the function f (x) and the function g (x) = x ^ 2 + X + a have exactly two different intersections on the interval [0,2], find the value range of real number a

Here is your analysis: 1) the definition domain of F (x) is (- OO, - 1) U (- 1, + OO), and the derivative f '(x) = 2 (x + 1) - 2 / (x + 1) = 2x (x + 2) / (x + 1), from F' (x) > 0, we get - 2

The monotone decreasing interval of the function y = (1 / 2) ^ (x ^ 2 + X + 2) is