© h.hofstede (h.hofstede@hogeland.nl) |
|||
![]() |
|||
1. | a. | f(x) =
-4x2 + px + 2p f '(x) = -8x + p = 0 p = 8x f(x) = -4x2 + 8x · x + 16x f(x) = 4x2 + 16x |
|
b. | f(x) = x3
- 12px -
15 f '(x) = 3x2 - 12p = 0 12p = 3x2 p = 1/4x2 f(x) = x3 - 3x3 - 15 f(x) = -2x3 - 15 |
||
c. | f(x) = 2px2
+ x -
p f '(x) = 4px + 1 = 0 4px = -1 p = -1/(4x) f(x) = -2/(4x) · x2 + x + 1/(4x) f(x) = 1/2x + 1/(4x) |
||
2. |
![]() |
||
Dat is nul als de teller
nul is: 2x(2 - px)
+ px2 = 0 4x - 2px2 + px2 = 0 4 - px2 = 0 px2 = 4 p = 4/x² |
|||
![]() |
|||
3. | y = ax2
+ bx + 8 y '= 2ax + b = 0 b = -2ax y = ax2 - 2ax2 + 8 y = -ax2 + 8 en die moet door (4, 20) gaan 20 = -a · 16 + 8 a = -3/4 b = -2ax = -6 |
||