The Gradient Function
I am going to be investigating the function of the gradient. A function is a variable that depends on the value of other independent variables and the gradient is the steepness of a line or curve.
I am going to try to work out a formula that will calculate the gradient of any given line or curve; this will be the gradient function.
I already know of some methods that can be used to calculate the gradient, these are:
. The formula:
increase in y
increase in x
This formula represents the vertical value on the graph divided by the horizontal value. It can also be written as:
dy
dx
This notation demonstrates the rate of change at y with respect to x. Which means that as x changes so does y. When using this formula to work out the gradient at of a curve a tangent must first be drawn.
2. 'Omnigraph' is a computer program which will create a graph for a given a formula. It will then draw tangents on the graph and work out the gradient.
3. The small increment method can be used as a more accurate way of calculating the gradient of a graph. To use it you must zoom in on a section of the graph, for example the coordinates (3,9) and (3.1,9.61). You connect the two points together using a straight line and because the graph is on a much larger scale the line should follow almost the same path as the curve. You then use the formula increase in y to calculate the gradient.
I am going to be investigating the function of the gradient. A function is a variable that depends on the value of other independent variables and the gradient is the steepness of a line or curve.
I am going to try to work out a formula that will calculate the gradient of any given line or curve; this will be the gradient function.
I already know of some methods that can be used to calculate the gradient, these are:
. The formula:
increase in y
increase in x
This formula represents the vertical value on the graph divided by the horizontal value. It can also be written as:
dy
dx
This notation demonstrates the rate of change at y with respect to x. Which means that as x changes so does y. When using this formula to work out the gradient at of a curve a tangent must first be drawn.
2. 'Omnigraph' is a computer program which will create a graph for a given a formula. It will then draw tangents on the graph and work out the gradient.
3. The small increment method can be used as a more accurate way of calculating the gradient of a graph. To use it you must zoom in on a section of the graph, for example the coordinates (3,9) and (3.1,9.61). You connect the two points together using a straight line and because the graph is on a much larger scale the line should follow almost the same path as the curve. You then use the formula increase in y to calculate the gradient.