Add maths problems on maxima and minima

ZaiDancerz SG

hi guys.. i dont even know how to start to slove this problems can anyone help me out?

jonchao72 SG

mind posting a sample question?

ZaiDancerz SG

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?

MyPillowTalks SG

http://justmathtutoring.com/

You may want to click the link on the left about calculus, and watch them

Seowlah SG

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.

ZaiDancerz SG

ok gt some idea.. But for number 2 how do u know which must express to something and sub. to which equation??

Seowlah SG

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.

ZaiDancerz SG

still blur ...

Seowlah SG

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

ZaiDancerz SG

giv up zzzzzzzzzzzzzz

Seowlah SG

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.