Find intervals while function is increasing or decreasing, Mathematics

Find out all intervals where the given function is increasing or decreasing.

f ( x ) = - x5 + 5/2 x4 + 40/3 x3 + 5

Solution

To find out if the function is increasing or decreasing we will required the derivative.

f ′ ( x ) = -5x4 + 10x3 + 40x2

= -5x2 ( x2 - 2x - 8)

= -5x2 ( x - 4) ( x + 2)

Note as well that while we factored the derivative first we factored a "-1" out to make the rest of the factoring a little bit easier.

From the factored form of the derivative we illustrates that we have three critical points :x = -2 ,x = 0 , and x = 4 .  We'll require these in a bit.

Now we have to determine where the derivative is +ve and where it's -ve..  As the derivative is a polynomial this is continuous and thus we know that the only way for it to change signs is to primary go through zero.

In other terms, the only place that the derivative might change signs is at the critical points of the function.  Now we've got another utilizes for critical points.  Thus, we'll build a number line, graph the critical points & pick test points through each region to illustrate if the derivative is positive or negative in each of region.

Following is the number line & the test points for the derivative.

316_function 1.png

Ensure that you test your points in the derivative. Recall that we know that the derivative will be the similar sign in each of region. The only place that the derivative can alter signs is at the critical points & we've marked the only critical points onto the number line.

Thus, it looks we've got the given intervals of increase & decrease.

Increase : - 2 < x <0 and 0 < x < 4

Decrease : - ∞ < x < -2 and 4 < x < ∞

Posted Date: 4/12/2013 6:02:12 AM | Location : United States







Related Discussions:- Find intervals while function is increasing or decreasing, Assignment Help, Ask Question on Find intervals while function is increasing or decreasing, Get Answer, Expert's Help, Find intervals while function is increasing or decreasing Discussions

Write discussion on Find intervals while function is increasing or decreasing
Your posts are moderated
Related Questions
A MANUFACTURING UNIT IS INTERESTED IN DEVELOPING A BENEFIT SEGMENTATION OF THE CAMERA MARKET. SUGGEST SOME MAJOR BENEFIT SEGMENT WITH MARKET TARGETING STRATEGIES?


como realizar la i elevavda a la 243

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?

A professor is interested in decisive if attending college influences the level at which an individual cooperates with the police. The professor is not sure  if attending college w

The time in seconds that it takes for a sled to slide down a hillside inclined at and angle θ is where d is the length of the slope in metres. Find the time it takes to sli

Illustrates that the following numbers aren't solutions to the given equation or inequality. y = -2 in 3( y + 1) = 4 y - 5 Solution In this case in essence we do the sam

A sell a watch to B at gain of 20% and B sell to C at loss of 10%. if C pays @ 432, how much did A pays for it.

What is a marketing plan

what states and marketing tasks?