2/3H H WATER SAND An oil rig of height H metres is located in the ocean. One-quarter of the rig is in the sand, 4 metres is in the water and two-thirds of it is in the air.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
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Simple equations
1.
2/3H
H
WATER
SAND
An oil rig of height H metres is located in the ocean. One-quarter of the rig is
in the sand, 4 metres is in the water and two-thirds of it is in the air.
(a)
Write an equation, in terms of H, to répresent this data.
[1]
(b)
Solve your equation to find the height of the oil rig.
[4]
2
Jerry had $100. He went to a Computer Store, a Book Store and a Music Store. He spent three times
as much money in the Computer Store as he did at the Music Store. He spent $12 less at the Book
Store than at the Music Store. He then had $37 left.
(a)
Using x to represent the amount he spent at the Music Store, express in terms of x,
(i)
the amount spent at the Computer Store,
[1]
(ii)
the amount spent at the Book Store.
[1]
(b)
Form an equation in terms of x for the total amount of money spent.
[1)
Solve the equation formed in (b) to determine the amount of money spent at the Music
Store.
(c)
[2]
3
A triangle has sides of length x + 2, 2x + 3 and 3x + 2 centimetres, and an altitude
of x centimetres.
NOT TO
x + 2
2r + 3
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