Is the existence of partial derivative the same as the existence of partial derivative? (function of two variables)

1. The existence of partial derivative is different from that of partial derivative, which means that if partial derivative doesn't exist, it can't be calculated or calculated. Since partial derivative can be calculated, of course partial derivative must exist before it can be calculated

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1. 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?
2. If f ′ (x0) = - 3, then Lim [f (x0 + H) - f (x0-3h)] / h= process
3. If f ′ (x0) = - 3, then limh → 0f (x0 + H) - f (x0-h) H = () A. -3B. -6C. -9D. -12
4. If f ′ (x0) = - 2, then Lim [f (x0 + H) - f (x0-h)] / h=
5. When Lim h tends to zero, (f (x0 + H) - f (x0-h)) / 2H = f '(x0) can't understand
6. If f (x) is differentiable at point X and lim f (x-3h) - f (0) / h = 1, then f '(x) =? H-0
7. Let f (x) be differentiable at x = 2 and f '(2) = 2, then Lim h → 0 [f (2-3H) - f (2)] / h =?
8. If the function f (x) is differentiable at x = a, then Lim h → 0 (f (a + 3H) - f (A-H)) △ 2H =?
9. Let f (x) be differentiable at x = 1 and f '(1) = 2, then [LIM (H → 0) f (1-h) - f (1)] / h is equal to
10. Let f (x) be differentiable at x = A and lim [f (a + 5H)] - f (a-5h)] / 2H = 1, then f '(a)=
11. 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.)
12. 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
13. 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?
14. 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
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