differentiation find the difference between maximum and minimum heights
Using differentiation find the difference between maximum and minimum heights for both the roller coasters.
1. The brochure for the Feel the Fear coaster says that the height of the coaster can be determined by this polynomial model for 12 seconds after the coaster comes out of a loop
Find the maximum and minimum heights.
Draw the graph (by hand) When is the coaster at ground level? Confirm using factor theorem.
2. The Giant coaster is modeled by
The height of the coaster can be determined for the first 12 seconds of the ride by this polynomial.
Calculate maximum and minimum heights using differentiation then draw the graph(by hand)
Where does the ride start?
The ride has 100 metres of fencing to make a rectangular enclosure as shown. It will use existing walls for two sides of the enclosure, and leave an opening of 2 metres for a gate.
a Show that the area of the enclosure is given by:
A = 102x – x2
b Find the value of x that will give the maximum possible area.
C Calculate the maximum possible area
Snacks will be provided in a box with a lid (made by removing squares from each corner of a rectangular piece of card and then folding up the sides)
You have a piece of cardboard that is 40cm by 40 cm – what dimensions would give the maximum volume?
Q1)
Put the derivativeequal to zero.
This means that
To find out maximum or minimu point, we will find second derivative
At t=8
This is negative and it is maximum point
The maximum coordinates of the point are (36, 8)
Now at
T = 3.3
It is positive so t = 3.3 gives the minimum point (-14.8,3.3)
b)
c)
By synthetic division
2 -1 17 -80 100
-2 30 -100
-1 15 -50 0
Because h(2) gives the zero remainder so function is (t-2)
-t2+15t-50
for t=2
for t=10
for t=5
At t = 2,5 or at t = 0 the roller coaster will be at the ground level.
It is can also be seen from the graph
Q2)
a)
The derivative is zero for maximum or minimum point
By quadratic formula
To get the maximum and the minimum point we will differentiate it again
For t=8.21 and 1.8 this will become
Second derivative is negative for t=8.21 and therefore it is a maximum point (-96.44, 8.21)
For t=1.8 it is positive so the minimum point is (36.432,1.8)
b)
The rider start at the height of -4400 at the t=-11.80 sec. The rider is at the zero point when the t is at 0 and 11.
Q3)
a)
Area of the rectangle=length x width
b)
The second derivative is
This is maximum point because the second derivative is negative so the maximum point is (51, 51).
c)
For maximum area, x=51
Q4)
a)
The volume of the rectangle is V
By using quadratic formula
At x=20
and
x=6.66
34.
Describe what is meant by ‘Business Process Management’ in relation to contemporary organisations
Describe what is meant by ‘Business Process Management’ in relation to contemporary organisations