Find the maximum and minimum of the function f (x) = x squared by e to the - x power

Find the maximum and minimum of the function f (x) = x squared by e to the - x power

f(x)=x²e^(-x)
f'(x)=(2x-x²)e^(-x)
From F '(x) = 0, we get x = 0, 2
F (0) = 0 is the minimum
F (2) = 4E ^ (- 2) is the maximum

What is the value of 2 (the second power of x) - 3xy + 7 (the second power of Y) - 3xy + 2 (the second power of Y)?

∵ Y: x = 2 / 7, y = 7x / 22 (the 2nd power of x) - 3xy + 7 (the 2nd power of Y) - 3xy + 2 (the 2nd power of Y) = (X & # 178; - 21x & # 178 / 2 + 49y & # 178 / 2) / (2x & # 178; - 21x & # 178 / 2 + 343x & # 178 / 4) = 15x & # 178; / (309x & # 178 / 4) = 60 / 309 = 20 / 103

The quadratic power of (x + y) is 18, and the quadratic power of (X-Y) is 6. Find the value of the quadratic power of X + 3xy + y

x²+2xy+y²=18
x²-2xy+y²=6
subtract
4xy=12
xy=3
So the original formula = (X & # 178; + 2XY + Y & # 178;) + XY
=18+3
=21

If the function f (x) = 1 / 3 (A-1) x ^ 3 + 1 / 2aX ^ 2-1 / 4x + 1 / 5 has an extreme point in its domain, then the value range of a

F (x) = 1 / 3 (A-1) x ^ 3 + 1 / 2aX ^ 2-1 / 4x + 1 / 5 has the extremum in its domain. F '(x) = (A-1) x ^ 2 + AX-1 / 4 has the solution △ = a ^ 2-4 * (A-1) * (- 1 / 4) > = 0A ^ 2 + A-1 > = 0, let a ^ 2 + A-1 = 0 (a + 1 / 2) ^ 2 = 5 / 4A = - √ 5 / 2-1 / 2A > = √ 5 / 2-1 / 2A