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## Derivatives

A derivative is simply a rate of change. Whether you're modeling the movement of a particle or a supply/demand model, this is a key instrument of Calculus.

# Linear Functions

If $$f(x)=8x+\frac{7}{19},$$ what is the value of $$f'(x)?$$

If $$f(x)=11x-17,$$ what is $$f'(5)?$$

If $$f(x)$$ is a linear function and $$f'(-11)=17,$$ what is the value of $$f'(11)?$$

If $$f(x)$$ is a linear function with $$f(5)=60$$ and $$f'(5)=3,$$ what is the value of $f(-3)+f'(-3)?$

If $$f(x)$$ and $$g(x)$$ are two linear functions with $$f'(1)=-5$$ and $$g'(1)=8,$$ what is the value of the derivative of the function $$f(x)-2g(x)$$ at $$x=1?$$

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