Utilizes second derivative test to classify critical point, Mathematics

Assignment Help:

Utilizes the second derivative test to classify the critical points of the function,

                                              h ( x ) = 3x5 - 5x3 + 3

Solution

The second derivative is,

                           h′′ ( x ) + 60x3 - 30x

The three critical points (x = -1, x = 0, & x = 1) of this function are all critical points where the first derivative is zero therefore we know that at least we have a possibility that the Second Derivative Test will work. For each of these the value of the second derivative is,

                h′′ ( -1) = -30                            h′′ (0) = 0              h′′ (1) = 30

The second derivative at x = -1 is -ve the second derivative at x = 1 is +ve and therefore we have a relative minimum here by the Second Derivative Test

In the case of x = 0 the second derivative is zero and therefore we can't utilizes the Second Derivative Test to classify this critical point.


Related Discussions:- Utilizes second derivative test to classify critical point

Ratio-categories of situations requiring division , Ratio - situations in ...

Ratio - situations in which we need to compare two quantities in terms of their ratio. (e.g., if Munna weighs 40 Kg. and Munni weighs 50 Kg., find the ratio of their weights.)

Pendulum, how many pendulum swings will it take to walk across the classroo...

how many pendulum swings will it take to walk across the classroom

Probability, Q)  In a lottery ,a person chooses six different natural numbe...

Q)  In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win

Determine the eigenvalues and eigenvectors of the matrix, Determine the eig...

Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require

Linear equations in one variable, three prices are to be distributed in a q...

three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of

The prerequisites for multiplication, THE PREREQUISITES FOR MULTIPLICATION ...

THE PREREQUISITES FOR MULTIPLICATION : The word 'multiply', used in ordinary language, bears the meaning 'increase enormously For instance, bacteria multiply in favourable conditi

Evaluate this integral value, The base of a right cylinder is the circle in...

The base of a right cylinder is the circle in the xy -plane with centre O and radius 3 units. A wedge is obtained by cutting this cylinder with the plane through the y -axis in

Determine the head loss, A 3 km pipe starts from point A end at point B ...

A 3 km pipe starts from point A end at point B Population = 3000 people Q = 300 L/day/person Roughness = cast ion pipe Length of the pipe = 3km Case 1 From A to B

Point, what will be the activity of the above said title

what will be the activity of the above said title

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd