hi guys.. i dont even know how to start to slove this problems can anyone help me out?
mind posting a sample question?
i duuno all this type of questions lol. i duuno for exmaple what must be subject and alot other things... any clear steps to follow?
You may want to click the link on the left about calculus, and watch them
Originally posted by ZaiDancerz:i duuno all this type of questions lol. i duuno for exmaple what must be subject and alot other things... any clear steps to follow?
1. Usually, the question will ask you to form an equation eg z in terms of x.
2. Or you are given 2 equations eg z in terms of y and x and y in terms of x.
You will need to express y in terms of x and substitute it into the first equation
so that z will be a function of x only.
3. Next, dz/dx = 0 for stationary points ie max pt, min pt and point of inflextion
4. Next solve for x and substitute the x value into z to find the z value.
This (x, z) will be the stationary point.
5. To determine the nature of stationary points, substitute x-, x and x+ into dz/dx to
identify the shape to see whether the stationary point is a max pt, min pt or point
of inflexion. Alternatively, find d2z/dx2 and subtitute the x value into it. If the
answer is negative, the stationary point is a max point. If the answer is positive,
the stationary point is a min pt.
6. If the question asks for max or min value, then just give the z value in the
stationary point.
ok gt some idea.. But for number 2 how do u know which must express to something and sub. to which equation??
Originally posted by ZaiDancerz:ok gt some idea.. But for number 2 how do u know which must express to something and sub. to which equation??
To express y in terms of x or express x in terms of y will depend on the question.
Next, substitute it into z whereby z has two unknowns x and y.
For example, the question asks you to find the maximum value of z for
the corresponding x value. You will need to express y in terms of x and substitute
it into z, dz/dx = 0, solve for x and subtitute x value into z to find max z value.
You will need to show that this value is a maximum by using step 5.
still blur ...
Question
The variables x and y are such that x4y = 8. A third variable is defined by
z = x + y.
Find the values of x and y that gives z a stationary value and show that this value is a minimum.
Steps
1. Express y in terms of x
x4y = 8
y = 8/x^4
2. Substitute y = 8/x^4 into z
z = x + y
z = x + 8/x^4
3. dz/dx = 1 - 32/x^5
For stationary value, dz/dx = 0
So, 1 - 32/x^5 = 0
x^5 = 32
x = 2
4. Substitute x = 2 into y
y = 8/x^4
y = 8/2^4
y = 0.5
5. Subst x = 2 and y = 0.5 into z
z = x + y
z = 2 + 0.5
z = 2.5
6. To show that z = 2.5 is a minimum value
d2z/dx2 = 160/x^6
Substitute x = 2 into d2z/dx2
= 160/2^6
Since d2z/dx2 > 0 ie this value of z = 2.5 is a minimum value
7. Hence, when x = 2 and y = 0.5, z = 2.5 is a minimum value
giv up zzzzzzzzzzzzzz
Originally posted by ZaiDancerz:giv up zzzzzzzzzzzzzz
I also give up liao le.
But seriously, your Add Maths foundation is very weak.
You need help from someone who will guide you step by step from the very basic concepts with a lot of examples and explanations.
Try to seek the help from your classmates who are very good in Add Maths or stay back everyday to seek help from your Add Maths school teacher.