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Finding maximum number of extrema

How does one find the local extrema of the function $x^1-x$?Finding local extrema of $f(x) = x^2 e^-x$Extrema of quartic functions $f(x)=ax^4+bx^3+cx^2+dx$ with $a>0$, $c<0$Lagrange multipliers and the extrema of $f(x,y) = -x^2-y^2+x+y$What's the Maximum Number of Local Minima an Nth-Order Polynomial Surface or Solid Can Have?Finding maximum and minimum with given constraintsFinding local maximum of solution of a differential equationCalculation of extrema pointsMultiple minima points and no maximumMaximum possible number of extrema of the function?

0

$begingroup$

This question appeared in JEST 2019

Question ->

$$g(x)= f(x)e^-(x^4+2x^2)$$

Find maximum number of extrema where $f(x)$ is a $k$th order polynomial.

I found $g'(x)$ and found

$$g'(x)= f(x)(-4x^3-4x) + f'(x)=0$$
for extrema

This equation has at least two complex roots. So maximum number of extrema should be $k+1$ but the answer is $k+3$.

maxima-minima

share|cite|improve this question

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How do you know it has at least two complex roots?
  $endgroup$
  – Paul Sinclair
  Feb 22 at 1:52
  

  
  
  
  

add a comment | 

0

$begingroup$

This question appeared in JEST 2019

Question ->

$$g(x)= f(x)e^-(x^4+2x^2)$$

Find maximum number of extrema where $f(x)$ is a $k$th order polynomial.

I found $g'(x)$ and found

$$g'(x)= f(x)(-4x^3-4x) + f'(x)=0$$
for extrema

This equation has at least two complex roots. So maximum number of extrema should be $k+1$ but the answer is $k+3$.

maxima-minima

share|cite|improve this question

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How do you know it has at least two complex roots?
  $endgroup$
  – Paul Sinclair
  Feb 22 at 1:52
  

  
  
  
  

add a comment | 

$begingroup$

This question appeared in JEST 2019

Question ->

$$g(x)= f(x)e^-(x^4+2x^2)$$

Find maximum number of extrema where $f(x)$ is a $k$th order polynomial.

I found $g'(x)$ and found

$$g'(x)= f(x)(-4x^3-4x) + f'(x)=0$$
for extrema

This equation has at least two complex roots. So maximum number of extrema should be $k+1$ but the answer is $k+3$.

maxima-minima

share|cite|improve this question

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

$endgroup$

share|cite|improve this question

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

share|cite|improve this question

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

edited Mar 10 at 20:42

Rodrigo de Azevedo

13k41960

asked Feb 21 at 16:12

user194259user194259

305

asked Feb 21 at 16:12

user194259user194259

305