# First Derivative

**Problem**

If the first derivative of the equation of a curve is a constant, the curve is:

A. circle | C. hyperbola |

B. straight line | D. parabola |

**Problem**

Determine the radius of curvature of the curve $x = y^3$ at point (1, 1).

A. 5.27 | C. 5.56 |

B. 5.65 | D. 5.72 |

**Problem**

Which of the following is the derivative with respect to *x* of $(x + 1)^3 - x^3$?

A. 6x + 3 |
C. 1 + 2x - 3x^{2} |

B. 3x^{2} + 2x + 1 |
D. 6x - 3 |

## Maxima and Minima | Applications

**Graph of the Function y = f(x)**

The graph of a function y = f(x) may be plotted using Differential Calculus. Consider the graph shown below.

As x increases, the curve rises if the slope is positive, as of arc AB; it falls if the slope is negative, as of arc BC.