Given the square of x-x-1 = 0, find the square of - 4x + 4x + 9 What is x?

Given the square of x-x-1 = 0, find the square of - 4x + 4x + 9 What is x?

one

When - 5 is less than or equal to X and less than or equal to 0, what are the maximum and minimum values of the square + 4x + 3 of y = x

The maximum is 8 and the minimum is - 1

Y = the square of x-4x + 5 (0 is less than or equal to X is less than or equal to 3) to find the maximum and minimum of the function

Question: y = x-4x + 5, (0 ≤ x ≤ 3), y = (X-2) - 4 + 5, that is y = (X-2) + 1, you can get the minimum value at x = 2, y = 1 at x = 0, you can get the maximum value at x = 5,

X ∈ [1,3], find the minimum and maximum of y = 4x square + 2 (x + 1) square + 1

Image method can be used
y=6x^2+4x+3
=6(x+1/3)^2+3/7
It can be seen from the image that y increases when x ∈ [1,3]
Then the minimum value f (1) = 13
Maximum f (3) = 59

Known x

y=4x+9/(4x-3)+2=4x-3+9/(4x-3)+2+3
=-[(3-4x)+9/(3-4x)]+5

Find the maximum value of function y = x + √ (4x-x ^ 2)

If the solution of 4x-x ^ 2 ≥ 0 is 0 ≤ x ≤ 4, then the definition field of X is [0,4]
For y, y '= 1 + (4-2x) / [2 √ (4x-x ^ 2)] let y' = 0, and x = 2 ± √ 2 can be obtained by simplifying calculation
However, if the definition field of X is [0,4], then x = 2 + √ 2, x = 0, x = 4 are respectively brought into the original formula y = x + √ (4x-x ^ 2), and the maximum result is 2 + 2 √ 2

Function f (x) = - x square + 4x + 3, X belongs to [a, a + 3], find the maximum value g (a) of F (x)

It belongs to the problem of axis definite interval motion of quadratic function. The opening is downward, and the axis of symmetry x = 2. In this case, we should talk about 1: when a 3 is less than 2, its maximum value g (a) = f (a 3) = - a bungalow-2a 6.2: when 2 is greater than a and less than a 3, its maximum value g (a) = f (2) = 7.3: when 2 is less than a, its maximum value g (a) = f (a) = - a square 4A 3

The maximum value of the function f (x) = - x square - 4x + 7 in the interval [- 3,4] is

F (x) = - x square - 4x + 7
=-(x²+4x+4)+11
=-(x+2)²+11
a=-1

The function f (x) is an odd function. When 1 ≤ x ≤ 4, f (x) = the square of X - 4x + 5, then when - 4 ≤ x ≤ - 1, the maximum value of function f (x) is?

1

The square of factoring factor x-4x-5
J urgent

x²-4x-5
=x²-5x+x-5
=x(x-5)+(x-5)
=(x-5)(x+1)