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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.


If \( f(x) = x^ {4} \), what is the value of \( f'(1) \)?

If \( f(x) = x^3 - 2x^2 + 3x +15 \) what is \( f'(14) \)?

\(f(x) \) is a quadratic function of the form \(f(x) = ax^2 + bx + c\), satisfying \(f(5) = 94\) and \(f’(x) = 6x + 3\), what is the value of \(a+b+c\)?

Details and assumptions

\(f’(x)\) denotes the derivative of \(f(x)\).

If \(f(x)=4x^2-12x+21\), what is the value of \(f'(14)\)?

If \(f(x)=x^3-4x^2+6x+18,\) what is \(f'(x)?\)


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