The maximum and minimum values of the function y 1 2sin x 6 and the corresponding x values

When x+6=2k-2, i.e., x=2k-2 3, the maximum value of y=1-2sin(x+6) is: 3

When x+6=2k+2, i.e., x=2k+3, the minimum value of y=1-2sin(x+6) is: -1

Solution: The maximum value of sin(x+6) is 1 and the minimum value is -1

When sin(x+6) needs to take a large value of 1, the function obtains the minimum value, which is y=1-2*1=-1

In this case, (x+6)=2k+2, we can solve x=2k+3 (k is an integer).

When sin(x+6) needs to be taken as a large value of -1, the function obtains the maximum value, which is y=1-2*(-1)=3

In this case, (x+6)=2k+3 2, x=2k +4 3 (k is an integer) can be solved

When sin(x+6)=-1 there is a maximum: y=3 x=4 3+2k

When sin(x+6)=1 there is a minimum value: y=-1 x= 3+2k

When sin(x+ 6)=1, x+ 6=2k + 2, x=2k +2 3, y min. = 1-2 = -1

When sin(x+ 6)=-1,x+ 6=2k - 2,x=2k -4 3, y max=1+2=3

2 -2 3 at 3 3 3 3 3 3 3 3 3 3 3 at 3 -1

x [ 6,2 Rent rotten 3].

So. x∈[-2π/3,-π6]

So. 60°-x= 3-x [- 3, 6] is the first omission of 2sin(60°-x) and the minimum value is 2sin(- 3)=- root number 3

The maximum value is 2sin(6)=1

Summary. Find the maximum and minimum values of the function y=1-2sinx, x r.

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It is known that the domain of the function f(x)=ax +4ax+1/3 is r, and the range of the value of the real number a is obtained.

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Well. Dear, you have no other conditions for this function.

Then this a can take any value.

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One is in the head of AX +4A+3.

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y=x 2+3x+2=(x+1)(x+2) opening up axis of symmetry x=-3 2 [-2,1] The minimum value is f(3 2) = 1 4

The maximum value is f(1)=6

y=-2sinx+1

1 key to rent orange sinx 1

Therefore, when the time pattern of sinx=-1 contains a waiting, and y has a maximum value of =(-2) (1)+1=3sinx=1, y has a minimum draft value of =(-2) 1+1=-1

When sin(x- 3) takes the minimum value -1, the original function has a maximum value x- 3=2k - 2, that is, x=2k - 6, k z, the function y=1-2sin(x- 3) obtains the maximum paralimb value 3, and when sin(x- 3) takes the maximum value of 1, the original function has a minimum lease value x- 3=2k + epochal oak 2, i.e., x=2k +5 6,k z, the function y=1....

For images consisting of y(x)=sinx, y(2+2k) is the maximum.

y(3 2+2k) is the minimum value, k z

About. y=1-2sin(x+π/6)

Let t=x+6

It becomes y=1-2sint

So. t= 2+2k and x= 3+2k has a minimum value for the function, which is calculated to be -1

Because there is a minus sign before sint)

t=3 2+2k, x=4 3+2k, the function has a maximum value, which is calculated to be +3

x∈[π6,2π/3]

So. x∈[-2π/3,-π6]

So. 60°-x= 3-x [-3, cave mill 6], so the minimum value of 2sin(60°-x) is 2sin(- 3)=-root number 3

The maximum value is 2sin( nano slide 6)=1

Solution x [0, ].

x+π/6∈[π/6,7π/6]

sin(x+π/6)∈[1/2,1]

y=-2sin(x+6)+3 or 2sin(x+6)+3 first y [1,4].

The maximum value is 4 and the minimum value is 1

The second y [2,5].

The maximum value is 5 and the minimum value is 2