022 Sample Final A, Problem 13

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Use differentials to find given

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 .


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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