Determine and classify all critical points , Mathematics

Assignment Help:

Determine and classify all the critical points of the given function.  Described the intervals where function is increasing & decreasing.

423_Classifying critical points.png

Solution: Firstly we'll require the derivative therefore we can get our hands on the critical points.  Note that we'll do some simplification on the derivative to help us find out the critical points.

g ′ (t ) = (t 2 - 4)(1/3)  +(2/3) t 2 (t 2 - 4)- 3

=(t 2 - 4)3  +     2t2 / 3(t 2 - 4)(2/3)

=3 (t 2 - 4) + 2t 2 /3(t 2 - 4)(2/3)

 =5t 2  -12 /3 (t 2 - 4)3

Thus, it looks like we'll have four critical points here. They are following,

t =± 2                                      here, the derivative doesn't exist.

t = ±√(12/5) = ±1.549             here, the derivative is zero here.

2026_critical point.png

Determining the intervals of increasing & decreasing will also give the classification of the critical points thus let's get those first.  Given is a number line along with the critical points graphed & test points.

Thus, we've got the given intervals of increasing & decreasing.

Increase : - ∞ < x - 2, - 2 < x < -√(12/5) , √(12/5) < x < 2,  &  2 < x < ∞

Decrease :  -√(12/5)

From this it looks like t = -2 & t = 2 are neither relative minimum or relative maximums as the function is increasing on both side of them.  Alternatively, t < -12   is a relative maximum and t =12 is a relative minimum.

Here is the graph of the function.

420_cp1.png


Related Discussions:- Determine and classify all critical points

Basic set union operation, Q. Basic Set Union Operation? Ans. Supp...

Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta

Show that x(q-r) + y(r-p) + z(p-q) = 0, If the p th , q th & r th term of...

If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans:    p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (

Statewide mortality rates, Assume that between workers exposed to asbestos ...

Assume that between workers exposed to asbestos in a shipyard in 1980, 33 died over a 10 year period from COPD, whereas only 24 such deaths would be expected based on statewide mor

Problems related to applying operations in learning maths, PROBLEMS RELATED...

PROBLEMS RELATED TO APPLYING OPERATIONS :  Some of us were testing Class 4 children with addition and subtraction problems. We gave them sums that were written horizontally and th

What is venn diagram, The diagrams drawn to given sets are called as Venn d...

The diagrams drawn to given sets are called as Venn diagrams or Eule -Venn diagrams. Here given the universal set U by points within rectangle and the subset A of the set U given b

Fft algorithm, (a) Using interpolation, give a polynomial f ∈ F 11 [x] of d...

(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which

Domain and range of a relation, Consider R be a relation from A to B, that ...

Consider R be a relation from A to B, that is, take R A Χ B. Then Domain R = {a: a € A, (a, b) € R for any b € B} i.e. domain of R is the set of all the first components of

Write 3.5 × 104 in decimal notation, Write 3.5 × 104 in decimal notation? ...

Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.

Inverse cosine, Inverse Cosine : Now see at inverse cosine.  Following is ...

Inverse Cosine : Now see at inverse cosine.  Following is the definition for the inverse cosine.                         y = cos -1 x       ⇔ cos y = x                   for

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