Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image whose derivative y = f '(x) passes through the point (- 2,0) (2 / 3,0), The minimum value of F (x) is - 8. Can (- 8,0) be brought in? Isn't the minimum a point with zero derivative? | Math enthusiast | Mathematical art

Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image whose derivative y = f '(x) passes through the point (- 2,0) (2 / 3,0), The minimum value of F (x) is - 8. Can (- 8,0) be brought in? Isn't the minimum a point with zero derivative?

If x = - 2 is the minimum of F (x), then f (- 2) = - 8A + 4b-2c = - 8F '(- 2) = 12a-4b + C = 0f' (2 / 3) = 4A / 3 + 4B / 3 + C = 0, the solution is a = - 1, B = - 2, C = 4, and the analytic expression of the function is f (x) = - X & # 179; - 2x & # 178; + 4x if x = 2 / 3

RELATED INFORMATIONS

1. Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through the point (- 2,0) (2 / 3,0) My equation is 64x3a-16b + C = 0 -8a+4b-2c=0 (8 / 27) a + (4 / 9) B + (2 / 3) C = 0, how to solve these three equations and find the process B = - C and what happened? Everybody speed... T-T
2. Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through points (- 2,0) and (2 / / 3,0), as shown in the figure (1) Finding the analytic expression of F (x) (2) If f (x) ≥ m ^ 2-14m holds for X ∈ [- 3,3], the value range of real number m is obtained (the picture shows: the opening of the image is downward, the intersection of the image and the X axis is - 2,2 / 3, and the intersection of the image and the Y axis is above.)
3. Is the existence of partial derivative the same as the existence of partial derivative? (function of two variables)
4. The existence of partial derivative of binary function, why can we deduce the following first 1. X - > x0 Lim f (x, Y0) = y - > Y0 Lim f (x0, y) 2. F (x, y) is differentiable at P0. If a function of one variable is differentiable, the curve is smooth. Why is it not that a function of two variables is differentiable? What is the geometric meaning of differentiable function of two variables?
5. If f ′ (x0) = - 3, then Lim [f (x0 + H) - f (x0-3h)] / h= process
6. If f ′ (x0) = - 3, then limh → 0f (x0 + H) - f (x0-h) H = () A. -3B. -6C. -9D. -12
7. If f ′ (x0) = - 2, then Lim [f (x0 + H) - f (x0-h)] / h=
8. When Lim h tends to zero, (f (x0 + H) - f (x0-h)) / 2H = f '(x0) can't understand
9. If f (x) is differentiable at point X and lim f (x-3h) - f (0) / h = 1, then f '(x) =? H-0
10. Let f (x) be differentiable at x = 2 and f '(2) = 2, then Lim h → 0 [f (2-3H) - f (2)] / h =?
11. Given that the derivative of the function f (x) = AX3 + bx2 + CX is even, then A f (x) is an even function B F (x) is an odd function C f (x) has both maxima and minima
12. How can we get the result of ∫ (upper Π / 4 lower 0) tanxdx = lncosx I (upper Π / 4 lower 0)?
13. What is the mathematical symbol and what does it stand for
14. [(12.56/3.14)^2*3.14/(4*3)]/(1^2*3.14)=1.3m ^
15. What does the mathematical symbol * stand for
16. How to express "or" with mathematical symbol
17. What does this mathematical symbol mean?
18. What does the mathematical symbol "∮" mean?
19. How to express every minute in mathematical symbols
20. (ln1/3+ln1+ln3+ln9+… +ln729)log3^e