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Increase and concavity of the function (derivatives)

-1

$begingroup$

Given $2$ functions:

$(a) $ $U(x) = -(b-x)^c$

$(b) $ $U(x) = ln(2+ln (x+5))$

For that $x, b$ or $c$ $$U'(x) > 0$$ and $$U''(x)<0?$$

(The answer may be, $f.$ ex. $a>0, b> x$ etc.)

My solution $:$

$(a) U'(x) = c(b-x)^c-1$ and

$U''(x) = -(c-1)c(b-x)^c-2.$

functions derivatives

share|cite|improve this question

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is you question?
  $endgroup$
  – Maria Mazur
  Mar 27 at 18:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I edited my question
  $endgroup$
  – Philip
  Mar 27 at 18:39
  

  
  
  
  

add a comment | 

-1

$begingroup$

Given $2$ functions:

$(a) $ $U(x) = -(b-x)^c$

$(b) $ $U(x) = ln(2+ln (x+5))$

For that $x, b$ or $c$ $$U'(x) > 0$$ and $$U''(x)<0?$$

(The answer may be, $f.$ ex. $a>0, b> x$ etc.)

My solution $:$

$(a) U'(x) = c(b-x)^c-1$ and

$U''(x) = -(c-1)c(b-x)^c-2.$

functions derivatives

share|cite|improve this question

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is you question?
  $endgroup$
  – Maria Mazur
  Mar 27 at 18:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I edited my question
  $endgroup$
  – Philip
  Mar 27 at 18:39
  

  
  
  
  

add a comment | 

$begingroup$

Given $2$ functions:

$(a) $ $U(x) = -(b-x)^c$

$(b) $ $U(x) = ln(2+ln (x+5))$

For that $x, b$ or $c$ $$U'(x) > 0$$ and $$U''(x)<0?$$

(The answer may be, $f.$ ex. $a>0, b> x$ etc.)

My solution $:$

$(a) U'(x) = c(b-x)^c-1$ and

$U''(x) = -(c-1)c(b-x)^c-2.$

functions derivatives

share|cite|improve this question

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

$endgroup$

share|cite|improve this question

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

share|cite|improve this question

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

edited Mar 27 at 18:42

Dbchatto67

2,419422

edited Mar 27 at 18:42

Dbchatto67

2,419422

asked Mar 27 at 18:36

PhilipPhilip

877

asked Mar 27 at 18:36

PhilipPhilip

877