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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

         

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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