First Derivative

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


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


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

A.   6x + 3 C.   1 + 2x - 3x2
B.   3x2 + 2x + 1 D.   6x - 3


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

A.   2 C.   4
B.   -2 D.   -4


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.

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