Difference between revisions of "022 Sample Final A, Problem 13"

From Math Wiki
Jump to navigation Jump to search
(Created page with "<span class="exam">Use differentials to find <math style="vertical-align: -4px">dy</math> given <math style="vertical-align: -4px">y = x^2 - 6x, ~ x = 4, ~dx = -0.5.</math> {...")
 
Line 1: Line 1:
 +
[[File:Differential.png|right|400px]]
 +
 
<span class="exam">Use differentials to find <math style="vertical-align: -4px">dy</math> given <math style="vertical-align: -4px">y = x^2 - 6x, ~ x = 4, ~dx = -0.5.</math>
 
<span class="exam">Use differentials to find <math style="vertical-align: -4px">dy</math> given <math style="vertical-align: -4px">y = x^2 - 6x, ~ x = 4, ~dx = -0.5.</math>
  
Line 14: Line 16:
 
::<math>dy\,=\,f'(x)\cdot dx,</math>
 
::<math>dy\,=\,f'(x)\cdot dx,</math>
 
|-
 
|-
|where we use a given <math style="vertical-align: 0px">x</math>-value to evaluate <math style="vertical-align: -5px">f'(x)</math>.
+
|where we use the given specific <math style="vertical-align: 0px">x</math>-value to evaluate <math style="vertical-align: -5px">f'(x)</math>.
 
   
 
   
  

Revision as of 21:41, 4 June 2015

Differential.png

Use differentials to find given

Foundations:  
When we use differentials, we are approximating a value for a function by using the slope of the derivative. The idea is that given a distance from a point , we can use , the slope of the tangent line, to find the rise, . Recalling that we can write
the relation is
where we use the given specific -value to evaluate .


 Solution:

Step 1:  
By the power rule, we have
We need to evaluate this at the given value , so
Step 2:  
We use the values given and the result from step 1 to find
Final Answer:  

Return to Sample Exam