Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific value into a function to determine its output. In this case, evaluating ƒ(x+h) means replacing 'x' in the function ƒ(x) = 6x + 2 with 'x+h', which allows us to analyze how the function behaves as 'h' changes.
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Difference Quotient
The difference quotient is a fundamental concept in calculus that represents the average rate of change of a function over an interval. It is calculated as [ƒ(x+h) - ƒ(x)]/h, which helps in understanding the slope of the tangent line to the function at a point as 'h' approaches zero.
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Limit Concept
The limit concept is crucial in calculus, particularly when analyzing the behavior of functions as they approach a certain point. In the context of the difference quotient, taking the limit as 'h' approaches zero allows us to find the derivative of the function, which represents the instantaneous rate of change.
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