Finding the derivative of function y = (2x ^ 2-3) (x ^ 2-4)

y=(2x^2-3)(x^2-4)
=2x^4-8x^2-3x^2+12
=2x^4-11x^2+12
y'=8x^3-22x

1. What is the relationship between the derivative y 'of function y = f (x) and the value and extremum of function?

Assume that the function is continuous and there is an x0 in the domain
When x

Solve the derivative and extremum of function f (x) = (x + 2) ∧ 2 (1-2x) ∧ 1 / 2

The answer is (x + 2) (1-2x) ^ 1 / 2 [2 + (x + 2) (1-2x) ^ 1 / 2]. For details, please refer to the derivation formula of product in mathematical analysis

Finding the extreme value of function y = x ^ 2 * e ^ (- x)

Derivation
y'=2x*e^(-x)-x^2*e^(-x)
Let y '= 0
2x=x^2
So x = 2, y = 4 / e ^ 2 maximum
Or x = 0, y = 0 minimum

The school needs 500 square bricks with a side length of 2 mm, and how many square bricks with a side length of 4 DM?

Suppose you need x bricks. According to the meaning of the question, 4 × 4x = 2 × 2 × 500 & nbsp; & nbsp; & nbsp; 16x = 2000 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 125 A: you need 125 such square bricks

If x + y = 1 / 2, then the minimum value of (1 / x) + (4 / y) is, using the mean value theorem?

To add x, y is a positive number (1 / x) + (4 / y) = [(1 / x) + (4 / y)] × 1 = [(1 / x) + (4 / y)] × [2 (x + y)] = 2 [1 + (Y / x) + (4x / y) + 4] ≥ 2 [5 + 2 √ (Y / x) (4x / y)] = 2 [5 + 4] = 18 if and only if (Y / x) = (4x / y), that is, x = 1 / 6, y = 1 / 3, the minimum value of (1 / x) + (4 / y) is 18

Why is the range of inverse trigonometric function limited and does not coincide with the original trigonometric function graph?

Because the anti trigonometric function is also a function, it must satisfy the definition of function. That is to say, for any value of an independent variable, there is a unique function value y corresponding to it
For a trigonometric function, for an X, there is only one y corresponding to it. On the contrary, for any y, there are many x corresponding to it. Therefore, we limit x to an interval to ensure that the inverse function also satisfies the definition of function
The inverse function and the image of the function are symmetric with respect to the line y = X

Cut the cube with the edge length of 2 cm into 8 cubes with the edge length of 1 cm, and increase the surface area by () square cm?
Come on!
Hurry!

Cut the cube with the edge length of 2 cm into 8 cubes with the edge length of 1 cm, and the surface area is increased by (24) square cm
8 × 6 × 1 × 1-6 × 2 × 2 = 24 square centimeter

In order to explore the "relationship between electric power and resistance", Xiao Ming found two L1 ` L2 bulbs with rated voltage of 3.8V and 2.5V respectively, and connected them in series. (sliding rheostat, voltmeter, ammeter, power supply, switch and wire) to explore. After closing the switch, he saw L1 emitting light slightly, L2 not emitting light, and immediately judged that L2 filament was broken, the reason was?

No. because two lamps are connected in series, if L2 filament is broken, then the whole circuit is open circuit and L1 should not light up

Finding the derivative of function y = (2x ^ 2-3) (x ^ 2-4)