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The first derivative is the slope of a curve, and the second derivative is the slope of the slope, like acceleration. So what's the third derivative? (Fun fact: it's actually called jerk.)

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In the above diagram, the red curve is the graph of a function \(f,\) and the blue curve is the graph of its first derivative \(f'.\) What is the relationship between \(f'(-1)\) and \(f''(1) ?\)

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Given the graph of \(y=f(x)\) above, which of the following is a possible graph of \(y=f''(x)?\)

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Find \(f^{(100)}(0)\). If

\[\large{ f(x) = \sin x + x^{100000}}\]

**Note:** \(f^n(x)\) denotes the \(n^{th}\) derivative of \(f(x)\).

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