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# Curve Sketching

You don't need a calculator or computer to draw your graphs! Derivatives and other Calculus techniques give direct insights into the geometric behavior of curves.

The graph of \(y = f(x)\) is shown. On which intervals is \(f'(x) > 0?\)

The graphs of \(y = g(x)\) and \(y = h(x)\) are shown above. Which is the derivative of the other?

On what intervals is \(f(x) = x^3 - 12x\) increasing?

\(A = (-\infty, -2)\)

\(B = (-2, 2)\)

\(C = (2, \infty)\)

Interval | Sign of \(f'(t)\) |

\((0,1)\) | + |

\((1,2)\) | - |

\((2,3)\) | - |

\((3,4)\) | + |

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