Relative maximum point, Mathematics

Relative maximum point

The above graph of the function slopes upwards to the right between points C and A and thus has a positive slope among these two points. The function has a negative slope between points E and C. So at point C, the slope of the function is Zero.

Among points X1 and X2    ((dy)/(dx)) > 0; whereas X1 ≤ X < X2

And among X2 and X3   ((dy)/(dx)) < 0; Whereas X2 < X ≤ X3.

Therefore the first test of the maximum points which needs that the first derivative of a function equals zero or

(dy)/(dx) = f'(x) < 0

The second text of a maximum point which needs that the second derivative of a function is negative or

            (d2y)/(dx2) = f''(x) < 0

 

Illustration

Find out the critical value for the given functions and determine the critical value that constitutes a maximum

            y = x3 - 12x2 + 36x + 8

Solution

            y = x3 - 12x2 + 36x + 8

            Then    (dy)/(dx) = 3x2 - 24x + 36 +0

i.                    The critical values for the function are acquired by equating the first derivative of the function to zero, which is as:

(dy)/(dx) =  0 or 3x2 - 24x + 36 = 0

Thus (x-2) (x-6) = 0

And also x = 2 or 6

The critical values for x are x = 2 or may be 6 and critical values for the function are y = 40 or maybe 8

i.                    To ascertain where these critical values of x will provides rise to a maximum that we apply the second text, which is :

(d2y)/( d2x)       < 0

(dy)/(dx) = 3x2 - 24x + 36 and

(d2y)/(d2x) = 6x - 24

a)      When x = 2

Then    (d2y)/( d2x)    = -12 <0

 

b)      When x = 6

Then    (d2y)/( d2x)    = +2 > 0

Therefore a maximum occurs when x = 2, as this value of x satisfies the second condition. X = 6 does not provides rise to a local maximum

Posted Date: 2/15/2013 6:42:59 AM | Location : United States







Related Discussions:- Relative maximum point, Assignment Help, Ask Question on Relative maximum point, Get Answer, Expert's Help, Relative maximum point Discussions

Write discussion on Relative maximum point
Your posts are moderated
Related Questions
Write down the equation of the line which passes through the points (2, -1, 3) and (1, 4, -3).  Write all three forms of the equation of the line. Solution To do the above


when i couulate the formula f 64 divided by 65 how do i do this

A car buyer has a choice of three makes, five body styles, and six colors. How many different choices does the buyer have?

question paper on fractions

Two 1000 liter tanks are containing salt water. Tank 1 has 800 liters of water initially having 20 grams of salt dissolved in this and tank 2 has 1000 liters of water and initially

Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.

I have a simple right angle triangle. All I am given is h (the hypotenuse) and that ratio of x:y is 2:3. What is the formula to find x and y in terms of h?

One box can hold 5 1/2 lbs of nuts and 3 lb 6oz of bolts. What is the total weight for one box?

If 2/3 of a number is 24 then 1/4 of a number is...