# Differential Calculus

**Problem**

A Toyota Land Cruiser drives east from point *A* at 30 kph. Another car, Ford Expedition, starting from *B* at the same time, drives S30°W toward *A* at 60 kph. *B* is 30 km from *A*. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A. 70 kph | C. 55 kph |

B. 80 kph | D. 60 kph |

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**Problem**

Find *y’* if *x* = 2 arccos 2*t* and *y* = 4 arcsin 2*t*.

A. 2 | C. 4 |

B. -2 | D. -4 |

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**Problem**

A parabola has an equation of *y*^{2} = 8*x*. Find the equation of the diameter of the parabola, which bisect chords parallel to the line *x* – *y* = 4.

A. y = 2 |
C. y = 4 |

B. y = 3 |
D. y = 1 |

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**Problem**

A point moves in the plane according to equations *x* = *t*^{2} + 2*t* and *y* = 2*t*^{3} - 6*t*. Find *dy*/*dx* when *t* = 0, 2, 5.

A. -3, -3, -12 | C. 3, 3, 12 |

B. 3, -3, 12 | D. -3, 3, 12 |

- Read more about Slope of a Curve of Given Parametric Equations
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