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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.

# Graphical Interpretation of Derivatives

The above graph represents the function $$y=g(x).$$ Judging the graph as well as you can by eye, what can we say about the derivatives of $$g(x)$$ at $$x=-2,0,2?$$

If the graph of $$y=f(x)$$ is as shown above, on which of the following intervals is the slope of the tangent line always positive?

Which of the following is a possible value for the slope of the tangent line to the above curve at point $$P=(1, 2) ?$$

If the equation of the tangent line at point $$Q$$ is $$y=0.924x+6,$$ which of the following is a possible value for the slope of the tangent line at $$P ?$$

The above diagram is the graph of a function $$f$$ satisfying $$f(-x) = -f(x)$$. If the slope of the tangent line at point $$O$$ is $$1.542$$ and the slope of the tangent line at point $$Q$$ is $$-1.316,$$ what is the slope of the tangent line at point $$P ?$$

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