Thursday

November 27, 2014

November 27, 2014

Posted by **Desperado** on Monday, January 11, 2010 at 2:55am.

I dont know the steps on how to do it! Can you please just tell me the steps?

Find the intervals on which the function is increasing and decreasing.

g(x) = x√((8-x)^2)

(also, what is the difference between local max/min and absolute max/min and can you have two local maximums(/mins) ?

thanks!!

- calculus -
**Desperado**, Monday, January 11, 2010 at 2:59amCORRECTION!

I read the problem wrong

..

its actually

g(x) = x√(8 - x^2)

the second x is the only thing that is squared not the whole (8-x).

sorry!

- calculus -
**MathMate**, Monday, January 11, 2010 at 11:49amThe maxima/minima are part of the important ingredients when we try to sketch the graph of a function without having to plot every possible point.

A local maximum of a function occurs at an interior point c (i.e. f(c+) and f(c-) exist) of its domain if f(x) ≤ f(c) for all x in some open interval containing c. The definition of local minimum is similar.

It is possible to have multiple local maxima/minima.

A global (absolute) maximum of a function occurs at a point c if f(x) ≤ f(c) for all x on its domain. the definition for global minimum is similar.

For example, the function y=x² has a local minimum at x=0. We note that y(0)=0, and at both x=0+ and at x=x-, the value of the function is greater than 0. Therefore x=0 is a local minimum for y=x².

However, there is no local (nor global) maximum for y=x², since for any value of y(x) corresponding to a particular value of x, we can find a greater value of y(x). Since x=±∞ is not in the domain of y=x², there is no local nor global maximum.

To find the local and global maxima/minima, it is necessary to follow these steps:

1. find the domain of the function.

2. Calculate all the critical points in the domain. A critical point is a point where the derivative f'(x) becomes zero,*or*or where f'(x) is undefined.

3. Since a local extremum can only occur at the following points:

a. interior point where f'(x)=0.

b. endpoints of the domain of f(x).

c. interior points where f'(x) is undefined.

So calculate the values of f(x) at all the critical points*and*at endpoints of the domain. From the calculated values of f(x), determine the local/global extrema.

**Answer this Question**

**Related Questions**

Physics Word Problems - Could you please explain to me these problems, I dont ...

math: inequalities - 2b < 8 My answer is that b is less than or equal to 3.9...

math ergent please please... - 10.a)Solve the inequality x^3-5x^2+2x+8<0 by i...

Calculus - Find the intervals where the function f(x)=((2x-1)^2)(x-3)^2 is ...

algr.1 - 1/4n+12>3/4n-4 solve the inequality and please show the steps I dont...

Fine Arts - Please i need help, Im trying so hard on this and i just cant do it...

Algebra 1 - (3xsquared-8x+1)(-2xsquared+-2) (i wrotee squared because i dont ...

math - ok so I asked a question like this before and I understood how to do it ...

Chemistry - Posted for Rudy - Posted by Rudy on Sunday, January 26, 2014 at 7:...

English - Mr Carter says we can't tell people about the steps in the sand. He ...