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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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