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Practical application of derivative (optimization problem in life)! When the volume of cylindrical metal beverage can is certain, how to choose its height and radius in order to save the materials?
Let the height h, radius r, v = h π R ^ 2, H = V / (π R ^ 2), the sum of the upper and lower areas is S1 = 2 π R ^ 2, the side area S2 = 2 π RH s = S1 + S2 = 2 π RH + 2 π R ^ 2 = 2V / R + 2 π R ^ 2 s' = - 2V / R ^ 2 + 4 π R, and the maximum value is s' = 0, v = 4 π R ^ 3, so h = 4R
If you want to make an open cylindrical container with a volume of 8 π, ask the bottom radius and height to save the most materials
let r be the radiush be the heightV= πr^2h = 8πh=8/r^2A = πr^2 + 2πrh= πr^2 + 16π/rA' =π(2r-16/r^2)=02r^3-16=0r=2A'' =π(2+32/r^3)A''(2)>0 ( min )min A at r =2h=8/r^2= 2
1、 U = 2x + 2Y + XY + 8 find u derivative x derivative y derivative 2、 U = 2 (x square) y find u derivative x derivative y derivative
(1)du/dx=2+y
du/dy=2+x
(2)du/dx=4xy
du/dy=2x ²
Y = the derivative of F (- x), then the derivative of Y is
Solution y = f (- x)
Then y '= [f (- x)]' = f '(- x)' = - f '(x)
The n-th derivative of arcsinx First find the first derivative, square both sides, and then find the N-2 derivative of the formula after square. What is the specific process of calculating with Leibniz formula according to this method
After the derivative is squared, the result is: 1 / (1-x ^ 2) = 1 / (1-x) * (1 + x); Split item: = 1 / 2 * (1 / 1-x + 1 / 1 + x); Then I believe you can see that the problem is transformed into finding the N-2 derivative of 1 / 1-x and 1 / 1 + X, which are regular and formula; For example: {1 / 1 + X} [n-2] = (- 1) ^ n-2 * (n-2)/ (1+...
How to find the derivative of polar coordinate equation? If Without transforming it into a rectangular coordinate equation thank you
The polar coordinate equation has two parameters: the module length R and the spoke angle T. therefore, the derivation of the polar coordinate equation r = R (T) is the same as the derivation process and method in the rectangular coordinate system, that is, the derivation of R from T. only the meaning of this derivative is different, which refers to the change rate of the module length R with respect to the spoke angle t
RELATED INFORMATIONS
- 1. The slope of the tangent is the value of the derivative at that point
- 2. Derivative: the derivative value of a point on the curve is the slope of the tangent line of the point on the curve. I don't understand this explanation. Please answer briefly
- 3. If the function f (x) = (e ^ x) - ax (E is the bottom of the natural logarithm). For any real number x, f (x) is greater than or equal to 1, find the value of the real number a
- 4. Given the function f (x) = Xe power (E is the bottom of natural logarithm), find the extreme value of function f (x)
- 5. Y = derivative of sin (3x + 5) How
- 6. lim(x->0)ln(1+2x)/e^x-1
- 7. Derivative problem: given the function f (x - 1 / x) = ln x, find the derivative of F (x) In parentheses is x minus x, not x minus 1
- 8. Derivative. If a point a (1,2) on y = 2x ^ 3 is known, then the tangent slope of point a is equal to? The derivative of y to X is y '(x) = (2x ^ 3)' = 6x ^ 2 How did you get this?
- 9. Derivative dy / DX of y = y (x) find the power of y of x = the power of X of Y?
- 10. It is known that f (x) is a differentiable function defined on (0, + ∞) and satisfies XF '(x) - f (x) ≥ 0. For any positive number a, B, if a > b, there must be () A. af（a）≤bf（b） B. bf（b）≤af（a） C. af（b）≤bf（a） D. bf（a）≤af（b）
- 11. When an object moves in a horizontal straight line, the distance (unit: m) after T seconds from the initial point is s (T) = 5t-2t ^ 2, then what is the initial velocity of the object? When does it have a speed of 0?
- 12. 1: The function f (x) = 1 / 2 x ^ 4 - 2x ^ 3 + 3M is known. If f (x) + 9 > = 0 is constant, the value range of real number m is? A.m >=3/2 B.m > 3/2 C.m
- 13. F (x) = - f (x + 3) find the period of this function Replace it with the form f (x) = f (x + n), where n is the period
- 14. The monotone decreasing interval of the function f (x) = the third power of X - the square of 3x + 2 is
- 15. Define the odd function f (x) of domain R, when x ∈ (－∞, 0), f (x) + XF '(x)
- 16. How to solve the equation The letter equality is also reduced to equal to 0. If constant = 0, how to solve it is not an inequality
- 17. The difference between derivative and differential
- 18. The area of a circle π R ^ 2 what are 2 π R and π D
- 19. How much is △ Y / △ x equal to if you know the 1 point (1, - 2) on the image with function f (x) = 2x ^ 2-4 and the adjacent point (1 + △ x, - 2 + △ y)
- 20. There are two factories a and B. factory a is located on the bank a of a straight river bank, factory B and factory a are on both sides of the river, factory B is located at B 40km away from the river bank, and the vertical foot d from factory B to the river bank is 50km away from a. the two factories shall jointly build a water supply station C on this bank. The cost of water pipes from the water supply station to factory a and factory B is 3A yuan and 5A yuan respectively, Where is the water supply station C built to save the water pipe cost?