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High school mathematics extreme value
(1) If y=2x-3+√( 13-4x) is known, then 13-4x≥0, that is, x≤ 13/4. Let m=√( 13-4x)≥0. /2+7/2

= - 1/2(m- 1)? +4≤4, when m=√( 13-4x)= 1, that is, x=3, y takes the maximum value of 4;

(2) It is known that y = (2 √ x-4)/(√ x+3) = 2-10/(√ x+3) ≥-4/3, and the minimum value is-4/3 when x=0;

(3) It is known that y=(2x? )/(x-3)=2/( 1/x-3/x? )=2/[-3( 1/x- 1/6)? +112], and x > 3, then y≥24, and the minimum value is 24 when x=6;

(4) It is known that y=x+4+√(9-x? ), let x=3cosθ and θ∈[0, π], then y = 3 (sin θ+cos θ)+4 ∈ [1, 4+3 √ 2], and find out the minimum and maximum values when x=-3 and 3/√2 respectively;

(5) Given that y=4x+9/x, the monotonically increasing interval of the function y is (-∞, -3/2] U [3/2, ∞], so the function y monotonically decreases in the interval (0, 1), that is, when x= 1, y takes the minimum value of 65430.

PS: As the landlord has explained, this is a math problem in high school. I haven't arrived at the university yet, so I don't need to seek guidance. I can solve it without guidance. I am calm upstairs. ...