Let f (x) = x (x-1) (x-a), (a > 1) find the derivative f '(x); & nbsp; and prove that f (x) has two different extreme points x1, x2

Let f (x) = x (x-1) (x-a), (a > 1) find the derivative f '(x); & nbsp; and prove that f (x) has two different extreme points x1, x2

F ′ (x) = (x-1) (x-a) + X (x-a) + X (x-1) = 3x2-2 (a + 1) x + A, ∵ △ = 4 (a + 1) 2-12a = 4a2-4a + 4 = 4 (a − 12) 2 + 3 ＞ 0, ∵ f ′ (x) = 0 must have two different real roots x1, X2, (let x1 ＜ x2) and ∵ f ′ (x) = have the opening of the image upward, ∵ - ∞＜ x ＜ x1, or x2 ＜ x ＜ + ∞, f ′ (x) ＞ 0, x1 ＜ x ＜ x ＜ x 2 There are three different extreme points x1, x2

How to calculate 99 × 52 simply?

99×52
=(100-1)×52
=100×52-52
=5200-52
=5148

Given that the distance from point P (x, y) to the origin is 1, then the trajectory of point Q (x + y, XY) is?

The above answers are not accurate enough
x²+y²=1
X=x+y
Y=xy
So x & # 178; - 2Y = 1
But we need to limit the range of X, y
x²+y²≥2|xy|
-1/2≤xy≤1/2
So the equation is X & # 178; - 2Y = 1, - 1 / 2 ≤ y ≤ 1 / 2

Decompose 99 into the sum of 19 prime numbers. The largest prime number can be ()

61
61 + 3*2 + 2*16

Finding the power series expansion of F (x) = arcsinx

Here's how to expand arcsinx. See the picture below for details
[1 + (x-1)] ^ (3 / 2) = x ^ (3 / 2) cannot be expanded into a power series of X. the function to be expanded into a power series of X must be infinitely differentiable at x = 0, and the second order and above derivatives of this function at x = 0 do not exist

According to statistics, recycling 5 tons of waste paper can make 4 tons of new paper, which is equivalent to protecting 85 trees. According to this calculation, recycling 120 tons of waste paper is equivalent to protecting several trees

120 / 5 × 4 × 85 = 8160 trees, a: Recycling 120 tons of waste paper is equivalent to protecting 8160 trees

Given the function f (x) = ax3-3x2 + 1, if f (x) has a unique zero point x0 and x0 > 0, then the value range of a is
How to do after finding the maximum and minimum?

What is the quotient of the sum of the largest one digit and its reciprocal divided by 8 / 9

(9+1/9)÷8/9
=82/9÷8/9
=41/4
=10.25

If 3x + ax + y-6y contains NO x term after merging the same term, then the value of a is

3x+ax+y-6y
=（a+3）x-5y
Because it doesn't contain x, so
a+3=0
a=-3

Li Bai went to get some wine. He took a walk on the street to pick up the pot. He drank half of the wine when he saw the flower. He added a bucket when he met the shop. He drank the wine when he met the shop and the flower three times. How much wine was there in the pot

Solution 1: equation: suppose that the original x-dou liquor in the pot is 2x-1 for the first time, 2 (2x-1) - 1 for the second time, and 2 [2 (2x-1) - 1] - 1 for the third time