Finding the range of function y = x2-2x + 2

Finding the range of function y = x2-2x + 2

y=x^2-2x+2=x^2-2*1*x+1-1+2=(x-1)^2+1
Range [1, + ∞)

Let f (x) be differentiable at x = 1, f (1) = 1, f '(1) = 3, then LIM (H) tends to 0 [F2 (1 + H) - F2 (1)] / ln (1 + H) = how much

F 2 (1 + H) written by Lou Zu should be the square of F (1 + H)
F ^ 2 (1 + H) is the square of F (1 + H)
When h → 0, ln (1 + H) is equivalent to H,
Then Lim [f ^ 2 (1 + H) - f ^ 2 (1)] / ln (1 + H)
=lim[f(1+h)+f(1)]*[f(1+h)-f(1)]/h
=lim2f(1)*f'(1)
=6

The function f (x) = the square of X + 2013 has a derivative at x = 2. In the process of finding f '(2), if the change of the independent variable is △ x, then the change of the function is △ y=

f(2+Δx)-f(2)=Δx(Δx+4)

Function y = C (C is a constant) when the independent variable x gets the change x0, △ y = f (x + △ x) - f (x) = C-C = 0, why? Is there a change
Why f (x + △ x) - f (x) = C-C

Because the image of y = C is a straight line parallel to the X axis, no matter what the value of X is y ≡ C, the values of F (x + △ x) and f (x) are unchanged, you can draw a picture to understand

How to judge whether the partial differential equation is linear or nonlinear

Let: the variable of partial differential equation is x (which can represent multiple variables), the function to be solved is y = y (x), z = Z (x), etc., and ABCD is a constant. Linearity means that the function to be solved and its derivatives (including the product of them and constants) are presented in the form of linear operation (addition and subtraction)

How to judge linear and nonlinear

A function with only y or Y derivative is linear, and it can have X function; but it can't have y and Y derivative in one term, similar to siny

On quadratic function in Mathematics
There is a triangle scrap iron whose vertex angle a is 30 degrees, ACB is 90 degrees, ABC is 60 degrees, ab = 12cm. Use this scrap iron to cut a rectangular iron sheet cdef, point D is on AC, point E is on AC, point F is on BC. To make the area of the cut rectangular iron sheet largest, where should point e be? Please give the detailed process. Good bonus points!

Let DC = x ∵ cdef be a rectangle ∵ EF = x and ∵ EF / AC = BF / BC ∵ BF = √ 3
/The maximum area is 9 √ 3, where e is the midpoint of ab

When X -, y decreases with the increase of X. when X -, y has a value (maximum or minimum), which is -

The second power of y = 2x + 6 when x

The problem of mathematical quadratic function
Y = - x * 2 + 2 (M + 1) x + m + 3 intersects the x-axis at a. B, where a is on the positive half axis of X and B is on the negative half axis
And AO = 3BO, find the value of M
It's a process
Don't why

Y = - x * 2 + 2 (M + 1) x + m + 3 intersects with X axis at a. B, where a is on the positive half axis of X, B is on the negative half axis of X, and AO = 3BO. Do not ask why the intersection of y = - x ^ 2 + 2 (M + 1) + m + 3 and X axis satisfies 0 = - x ^ 2 + 2 (M + 1) x + m + 3AO length = (M + 1) + root sign [(M + 1) ^ 2 + (M + 3)] Bo length = - (m + 1) + root sign [((M + 1) ^ 2 + (M + 3)] a

Y = 2x ^ 2, y = 2 (x-4) ^ 2 and y = 2 (x + 1) ^ 2
Draw their images in the same coordinate system
The symmetry axis and vertex coordinates of the viewing direction of each function image are removed respectively

Y = 2x ^ 2, up x = 0 (0,0)
Y = 2 (x-4) ^ 2 up x = 4 (4,0)
Y = 2 (x + 1) ^ 2 up x = - 1 (- 1,0)