How many monotone increasing intervals of function y = 1 / (3x ^ 3) - 3 (x ^ 2) + 5x

How many monotone increasing intervals of function y = 1 / (3x ^ 3) - 3 (x ^ 2) + 5x

I think the title should be: y = 1 / 3 (x ^ 3) - 3 (x ^ 2) + 5x
We can get y '= x ^ 2-6x + 5 by deriving the function
Let y '> 0, that is, x ^ 2-6x + 5 > 0
The solution is X5
The monotone increasing intervals of the original function are (- ∞, 1) and (5, + ∞)

How to solve the monotone increasing interval of function y = 1 / 3 (x ^ 3) - 3x ^ 2 + 5x?

Derivation:
y'=x^2-6x+5
Let y '> 0, that is, x ^ 2-6x + 5 > 0
(x-1)(x-5)>0
x>5,or,x

Given that the function f (x) = - X & # 179; + ax & # 178; + BX is in the interval (- 2,1), when x = - 1 is a de minimum and x = 2 / 3, take the maximum (1) to find the tangent equation of the corresponding point of the function y = f (x) when x = - 2

F '(x) = - 3x ^ 2 + 2aX + B. according to the meaning of the problem, the derivative of the function at x = - 1 and x = 2 / 3 is 0
Note: when the function obtains the extremum in the interval, the derivative is 0. In this problem, the cubic function has no point where the derivative does not exist
So: - 3-2a + B = 0, that is: 2a-b = - 3; and - 3 * (4 / 9) + 2A (2 / 3) + B = 0, that is: 4A / 3 + B = 4 / 3
So: a = - 1 / 2, B = 2. So the function is: F (x) = - x ^ 3-x ^ 2 / 2 + 2x
When x = - 2, y = 8-2-4 = 2, and f '(x) = - 3x ^ 2-x + 2, so f' (- 2) = - 8
So when x = - 2, the tangent equation passing through (- 2,2) is Y-2 = - 8 (x + 2), that is, 8x + y + 14 = 0

Given that the monotone increasing interval of quadratic function y = ax & # 178; + BX + C is (negative infinity, 2), find the monotone increasing interval of quadratic function y = BX & # 178; + ax + C

The monotone increasing interval of quadratic function y = ax & # 178; + BX + C is (negative infinity, 2), which means its opening is downward, that is A0, and the opening of quadratic function y = BX & # 178; + ax + C is upward, so its increasing interval is (- a / (2b), positive infinity), that is (- A / (- 4A * 2), positive infinity) = (- 1 / 8, positive infinity)

Let the function y = 2 – x – x ^ 3 find the monotone interval of the function, the concave convex interval find the extreme point and inflection point of the function, and make the image of the function

y=2–x–x^3
y'=-1-x^2
=-(1+x^2)