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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.

# Polynomials

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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