boredsatan
Member
- Joined
- Mar 23, 2017
- Messages
- 572
- Gender
- Male
- HSC
- 1998
Are my answers right?
r(x) = -200x^2 + 4800x
find r(x+h)
-200x^2 - 400xh -200h^2 + 4800x + 4800h
use differenetiation by first principles to find the equation of the rate of change in revenue respect to the month of the year
-400x + 4800
find the instantaneous rate of change in revenue at B (6,21600)
-400(6) + 4800 = 2400
find the equation of the tangent to the revenue at C (10,28000)
-400(10) + 4800 = -4000 + 4800 = 800
y = 800x + c
28000 = 800(10) + c
y = 800x + 20,000
2. p(x) = x^3 - 4x + 2
find p'(x)
3x^2 - 4
find p'(3)
3(3)^2 - 4 = 27-4 = 23
find the equation of the perpendicular line to p(x) at x = 3
p(3) = (3)^3 - 4(3) + 2 = 17
(3,17)
p'(3) = 3(3)^2 - 4 = 27-4 = 23
m1*m2 = -1
m1*23 = -1
m1 = -1/23
17 = -1/23(3) + c
c = 394/23
y = -1/23x + 394/23
use newton's methods to calculate the root of the equation x^3 - 4x + 2 = 0 that lies near x = 3. Express the answer correct to 3 decimal places
3. c(x) = (x^3 - 9x^2 + 26x - 24)/(x-3)
is the function continuous?
Yes, the function is continuous as it is drawn without lifting the pen of paper
calculate lim x (3) for c(x)
(x^3 - 9x^2 + 26x - 24)/(x-3) = (x-2)(x-3)(x-4)/(x-3)
= (x-2)(x-4)
= (3-2)(3-4)
= 1 * -1
= -1
4. The rate of change is expressed by s'(t) = 3x^2 - 36x + 72, x [0,12]. Find an expression for the total inventory, s(t) if the company had 200 items initially
6x - 36 + 200
b. Determine the area bounded by s'(t) and the x-axis between 2.54 ≤ t ≤ 9.46, correct to 2 decimal places
using calculus, 166.28
using the graph of the gradient, draw a sketch of a possible curve of s(t), label turning points, end points and intercepts
not sure about this question
r(x) = -200x^2 + 4800x
find r(x+h)
-200x^2 - 400xh -200h^2 + 4800x + 4800h
use differenetiation by first principles to find the equation of the rate of change in revenue respect to the month of the year
-400x + 4800
find the instantaneous rate of change in revenue at B (6,21600)
-400(6) + 4800 = 2400
find the equation of the tangent to the revenue at C (10,28000)
-400(10) + 4800 = -4000 + 4800 = 800
y = 800x + c
28000 = 800(10) + c
y = 800x + 20,000
2. p(x) = x^3 - 4x + 2
find p'(x)
3x^2 - 4
find p'(3)
3(3)^2 - 4 = 27-4 = 23
find the equation of the perpendicular line to p(x) at x = 3
p(3) = (3)^3 - 4(3) + 2 = 17
(3,17)
p'(3) = 3(3)^2 - 4 = 27-4 = 23
m1*m2 = -1
m1*23 = -1
m1 = -1/23
17 = -1/23(3) + c
c = 394/23
y = -1/23x + 394/23
use newton's methods to calculate the root of the equation x^3 - 4x + 2 = 0 that lies near x = 3. Express the answer correct to 3 decimal places
3. c(x) = (x^3 - 9x^2 + 26x - 24)/(x-3)
is the function continuous?
Yes, the function is continuous as it is drawn without lifting the pen of paper
calculate lim x (3) for c(x)
(x^3 - 9x^2 + 26x - 24)/(x-3) = (x-2)(x-3)(x-4)/(x-3)
= (x-2)(x-4)
= (3-2)(3-4)
= 1 * -1
= -1
4. The rate of change is expressed by s'(t) = 3x^2 - 36x + 72, x [0,12]. Find an expression for the total inventory, s(t) if the company had 200 items initially
6x - 36 + 200
b. Determine the area bounded by s'(t) and the x-axis between 2.54 ≤ t ≤ 9.46, correct to 2 decimal places
using calculus, 166.28
using the graph of the gradient, draw a sketch of a possible curve of s(t), label turning points, end points and intercepts
not sure about this question
