• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Absolute minimum and maximum

1. Homework Statement
FIND THE ABSOLUTE MINIMUM AND ABSOLUTE MAXIMUM OF:

f(x) = 9x + 1/x
on the interval [1,3]

2. Homework Equations



3. The Attempt at a Solution

I dont know how to get started!!!
 

lanedance

Homework Helper
3,304
2
hi silverbomb20 - any ideas or thoughts on what defines a maxima or minima?
 
i know i need to use the power rule to get it started, but i dont know how to apply it to the fraction..


derivative of x ^n is n * x^(n-1) right?

i know the 9x would go to just 9
but i am unsure about the fraction
 
32,580
4,310
Yes, d/dx(xn) = nxn-1. And 1/x = x-1, so you can use the power rule on that.
 

lanedance

Homework Helper
3,304
2
first part sounds good

so we're stuck on
[tex] \frac{d}{dx} (\frac{1}{x}) [/tex]

you could write it like below and use the power rule
[tex] \frac{d}{dx} (x^{-1}) [/tex]

or you could try and do it from first principles...
 
okay so would it be 9 + -1x^-2 ?

im a history major having a lot of trouble with calculus...please help me
 

lanedance

Homework Helper
3,304
2
yes, that looks correct

so when does

[tex] 9-\frac{1}{x^2} = 0 [/tex] ?
 
in my mind...never.

f1(x) = 9 + -1x^-2

so i have to set it equal to zero right?

so 9 + -1x^-2=0

but that doesnt factor
 
32,580
4,310
Multiply both sides by x^2.

Before we get (more) bogged down with minutiae, let's look at the strategy. Extreme values of a function f will happen at values of x for which f'(x) is zero, or at endpoints of the interval of definition.
 

lanedance

Homework Helper
3,304
2
f'(x) represents a critical point which could be a maxima, minima or point of inflection, but you nee dto check to find which

as we are talking about absolute max & min we also need to check the boundaries of [1,3] ie the points x=1 and x=3

as for the local minima you're on your way
9 + -1x^-2=0

try first multiplying both sides of the equation by x^2
 
okay so thats gonna give me 9x^2=x^2?

or does that -1x^-2 not cancel?
 

Related Threads for: Absolute minimum and maximum

Replies
5
Views
9K
Replies
5
Views
11K
Replies
1
Views
9K
  • Posted
Replies
2
Views
963
Replies
7
Views
7K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top