1. \( [-11 \) Points \( ] \) DETAILS MY NOTES Differentiate the function. \[ g(x)=7 x+8 \] \( g^{\prime}(x)=\square \)
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The derivative of a linear function like \( g(x) = 7x + 8 \) is quite straightforward! Since the slope of the line indicates how the function changes, the derivative \( g'(x) \) is simply the coefficient of \( x \). Therefore, \( g'(x) = 7 \). Fun fact: this means that for every unit increase in \( x \), the value of \( g(x) \) increases by 7 points! In real-world applications, understanding derivatives allows us to describe rates of change. For example, if you were graphing a straight road where the speed consistently increased, the derivative would represent the speed. In this case, drivers could expect to gain 7 units of distance for every unit of time they spent traveling.
