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What does the slope of the curve on a velocity time graph represent?
The rate of Change in acceleration.
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
What do the peaks of the graph represent?
They represent local maxima: points where small changes in the x-variable, in either direction, result in reductions in the y-variable.
What is calculus and what does it have to do with?
Calculus is a branch of mathematics which came from the thoughts of many different individuals. For example, the Greek scholar Archimedes (287-212 B.C.) calculated the areas and volumes of complex shapes. Isaac Newton further developed the notion of calculus. There are two branches of calculus which are: differential calculus and integral calculus. The former seeks to describe the magnitude of the instantaneous rate of change of a graph, this is called the derivative. For example: the derivative of a position vs. time graph is a velocity vs. time graph, this is because the rate of change of position is velocity. The latter seeks to describe the area covered by a graph and is called the integral. For example: the integral of a velocity vs. time graph is the total displacement. Calculus is useful because the world is rarely static; it is a dynamic and complex place. Calculus is used to model real-world situations, or to extrapolate the change of variables.
What would a graph look like Kelvin vs celsius?
Taking the x-axis to represent degrees C and the y-axis for K, it would be a straight line, parallel to y = x and with intercept (0, -273.15). The graph would not cross the y-axis.
