High school mathematics known function f (x) = root 3sin2x-2sin ² x-1 (1) Find the minimum positive period and minimum value of F (x); (2) If inequality | f (x) - M|

High school mathematics known function f (x) = root 3sin2x-2sin ² x-1 (1) Find the minimum positive period and minimum value of F (x); (2) If inequality | f (x) - M|

Note: F (x) = (√ 3) sin2x-2sin ² X-1 solution. (1) f (x) = (√ 3) sin2x-2sin ² X-1 = (√ 3) sin2x + cos2x-2 = 2Sin (2x + π / 6) - 2, so the minimum positive period of F (x) is π and the minimum value is - 4. (2) let t = f (x), when x ∈ (π / 12

Known function f (x) = A-1 / |x| (1) Verification: the function y = f (x) is an increasing function on (0, + ∞) (2) If f (x) Orz

Y = f (x) is an increasing function on (0, + ∞), a decreasing function on (- ∞, 0), and meaningless at 0
So, 0

Find the maximum and minimum values of the function y = 2Sin (2x + π / 3) (- π / 6 ≤ x ≤ π / 6), and write the set of X when obtaining the maximum value

Y = 2Sin (2x + π / 3) - π / 6 ≤ x ≤ π / 6 - π / 3 ≤ 2x ≤ π / 30 ≤ 2x + π / 3 ≤ 2 π / 3: 0 ≤ sin (2x + π / 3) ≤ 1, so: 0 ≤ 2Sin (2x + π / 3) ≤ 2, that is: 0 ≤ y ≤ 2. It can be seen that when the maximum value of Y is 2 and the minimum value is 0y = 2, 2x + π / 3 = π / 2, there are: when x = π / 12Y = 0, 2x + π / 3 = 0, there are: x =

Given the function f (x) = √ 3sin2x-2sin2x. If x ∈ [- π / 6, π / 3], find the maximum and minimum values of F (x) 2Sin (2x + π / 6) - 1 is simplified That's how to find the maximum and minimum

Explanation, solution, f (x) = 2Sin (2x + π / 6) - 1, is correct. I only explain the final result: F (x) = 2Sin (2x + π / 6) - 1 because x ∈ [- π / 6, π / 3] is known, so, - π / 3 ≤ 2x ≤ 2 π / 3, - π / 6 ≤ 2x + π / 6 ≤ 5 π / 6, y = SiNx, on X ∈ [- π / 6,5 π / 6], - 1 / 2 ≤ y ≤ 1

Find the minimum and maximum values of function y = 2x-1 / (x + 1) x belonging to [3,5]

Simplify the original function and get y = 2-3 / (x + 1). From the function formula, it can be seen that this is an inverse proportional function. Draw a sketch. From the graph, the function is monotonically increasing in the interval 3-5, so the minimum value of the original function is obtained when x = 3, and when x = 3, y = 1.25, while when x = 5, y takes the maximum value, and y = 1.5. In mathematics, the combination of numbers and shapes

Find the maximum and minimum values of the following functions, and find the set of X that makes the function obtain the maximum and minimum values (1) y = 3-2cosx (2) y = 2Sin (1 / 2x - π / 4 Please be more specific

Let me answer: the maximum value of trigonometric function in the whole domain is 1, and the minimum is - 1;
(1) The maximum value is 5, which is obtained when cosx = - 1. At this time, x = 2K π + π;
The minimum value is 1, which is obtained when cosx = 1. At this time, x = 2K π;
(2) Is y = 2Sin (x / 2 - π / 4)
The maximum value is 2, which is obtained when sin (x / 2 - π / 4) = 1... At this time, X / 2 - π / 4 = 2K π + π / 2, and the solution is x = 4K π + 3 π / 2;
The minimum value is - 2, which is obtained when sin (x / 2 - π / 4) = - 1... At this time, X / 2 - π / 4 = 2K π - π / 2, and the solution is x = 4K π - π / 2;
Hope to be useful to you!