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

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<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>

Latest revision as of 11:41, 6 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:  

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