Difference between revisions of "Math 22 Increasing and Decreasing Functions"

Revision as of 06:28, 28 July 2020

==Definitions of Increasing and Decreasing Functions.

 A function  is increasing on an interval when, for any two numbers  $x_{1}$  and 
  $x_{2}$  in the interval,  $x_{2}>x_{1}$  implies  $f(x_{2})>f(x_{1})$

 A function  is decreasing on an interval when, for any two numbers  $x_{1}$  and 
  $x_{2}$  in the interval,  $x_{2}>x_{1}$  implies  $f(x_{2})<f(x_{1})$

Test for Increasing and Decreasing Functions

 Let  $f(x)$  be differentiable on the interval  $(a,b)$ .
 1. If  $f'(x)>0$  for all  $x$  in  $(a,b)$ , then  $f$  is increasing on  $(a,b)$ .
 2. If  $f'(x)<0$  for all  $x$  in  $(a,b)$ , then  $f$  is decreasing on  $(a,b)$ .
 3. If  $f'(x)=0$  for all  $x$  in  $(a,b)$ , then  $f$  is constant on  $(a,b)$ .

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This page were made by Tri Phan

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-The page is under construction
+==Definitions of Increasing and Decreasing Functions.
+  A function  is increasing on an interval when, for any two numbers <math>x_1</math> and
+  <math>x_2</math> in the interval, <math>x_2>x_1</math> implies <math>f(x_2)>f(x_1)</math>
+  A function  is decreasing on an interval when, for any two numbers <math>x_1</math> and
+  <math>x_2</math> in the interval, <math>x_2>x_1</math> implies <math>f(x_2)<f(x_1)</math>
+==Test for Increasing and Decreasing Functions==
+  Let <math>f(x)</math> be differentiable on the interval <math>(a,b)</math>.
+. If <math>f'(x)>0</math> for all <math>x</math> in <math>(a,b)</math>, then <math>f</math> is increasing on <math>(a,b)</math>.
+. If <math>f'(x)<0</math> for all <math>x</math> in <math>(a,b)</math>, then <math>f</math> is decreasing on <math>(a,b)</math>.
+. If <math>f'(x)=0</math> for all <math>x</math> in <math>(a,b)</math>, then <math>f</math> is constant on <math>(a,b)</math>.
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

Difference between revisions of "Math 22 Increasing and Decreasing Functions"

Revision as of 06:28, 28 July 2020

Test for Increasing and Decreasing Functions

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