If the function f (x) = 2x & # 178; - MX + 3 is an increasing function on [- 2, + ∞) and a decreasing function on (- ∞, - 2], try to compare the size of F (- 1) and f (1)

If the function f (x) = 2x & # 178; - MX + 3 is an increasing function on [- 2, + ∞) and a decreasing function on (- ∞, - 2], try to compare the size of F (- 1) and f (1)

Combining with the image, we get that (x = - 2) is axisymmetric
f(－1)
It is known that f "(x) = 4x-m, and because the function has a minimum value at - 2 on the number axis, we take x = - 2 into 4x-m = O, so we get m = 8. That is, f (x) = 2x ^ 2-8x + 3. Finally, the symmetry axis of the quadratic function is 2, so f (- 1) is greater than f (1)
The function f (x) = 2x2 MX + 3 is an increasing function when x ∈ [- 2, + ∞), and a decreasing function when x ∈ (- ∞, - 2], then f (1) is equal to______ .
From the meaning of the question, we can see that x = - 2 is the axis of symmetry of F (x) = 2x2-mx + 3, that is - − M4 = - 2, ｜ M = - 8. ｜ f (x) = 2x2 + 8x + 3. ｜ f (1) = 13
If f (x) = 2x2-mx + 3, X (- 2, + ∞) is an increasing function and X (- ∞, - 2) is a decreasing function, then f (1)=______ .
∵ f (x) = 2x ^ 2-mx + 3 the axis of symmetry is x = m / 4 ∵ f (x) monotonically decreases on (- ∞, M / 4) ∵ f (x) is an increasing function on (- ∞, - 2) ∵ M / 4 = - 2 ∵ M = - 8, so f (1) = 13
The monotone increasing interval of function y = x square + 1 is?
[0, + ∞) monotone increasing (0, - ∞) monotone decreasing
f(x)=2(coswx)^2+2sinwxcoswx+1=cos2wx+sin2wx+2=sin(2wx+pai/4)+2
It seems that the last step is wrong
It should be the root 2 * sin (2wx + Pai / 4) + 2
Finding monotone interval of function y = - x square + 2|x| + 3
x≤0 y=-x^2-2x+3=-(x+1)^2+4
Single increase (- ∞, - 1], single decrease [- 1,0]
x≥0 y=-x^2+2x+3=-(x-1)^2+4
Single increase [0,1], single decrease [1, + ∞)
All in all
How can sin ^ 2wx become 1 / 2 (1-cos2wx)
Be more detailed, or I can't understand it
In the cosine double angle formula:
cos2x=1-2(sinx)^2
So ^ cos2x (1 / 2x)
You can change the X of the above formula to Wx
We don't know that the formula of double angle can be deduced from the cosine formula of sum of two angles
cos(x+x)=cosxcosx-sinxsinx=1-(sinx)^2-(sinx)^2=1-2(sinx)^2
What is a monotone interval of the square - 2x + 3 of the function y = x?
A quadratic function is a parabola. The coefficient of the square of X given by you is 1, greater than 0, and the opening is upward. The axis of symmetry is x = 2. The curve is divided into two parts: simple decreasing and simple increasing. Then, (- ∝, 2], (2, + ∝) are two monotone intervals of the function. Of course, their subintervals are monotone intervals of the function
How to simplify sin2wx + cos2wx + 2
I know that sin2wx + cos2wx + 2 = double of the root sign (sin2wxcos π / 4 + cos2wxsin π / 4) + 2 will go further, but I want to know how to get this step, especially π / 4
(COS π / 4 = sin π / 4 = 2 / 2)
Sin2wx + cos2wx + 2 = root 2 × 2 / 2 (sin2wx + cos2w) + 2
=Root 2 × (2 / 2 root 2sin2wx + 2 / 2 root 2cos2w) + 2
=(sin2wxcos π / 4 + cos2wxsin π / 4) + 2
Let f (x) = log take a as the base (1-A / x), where O1
1. Let g (x) = 1-A / x, because 01 = loga a
Because it's a decreasing function, so 1-A / X