The concept (and basic properties) of limits and derivatives
Want a deeper conceptual understanding? Try our interactive lesson!
No exercises available for this concept.
Practice exam-style limits and derivatives problems
The limit x→alimf(x) is the value f(x) approaches as x approaches a.
The IB may test your understanding of the gradient of the curve as the limit of
as (x2−x1) goes to zero.
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Given a table of values:
The derivative of f(x) is denoted f′(x) and is given by
For a curve y=f(x), f′(x) is the gradient or slope.
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You can graph f′(x) using the following steps:
Press the Y= key.
In one of the available function lines (e.g. Y_1), enter the expression for f(x).
In another available line (e.g. Y_2), input the derivative function usingMATH then 8:nDeriv( in the following format:
To enter Y1, press VARS then scroll to Y-VARS and select FUNCTION then Y1.
Press GRAPH to display both the original graph f and the derivative f′.
The graph of f′ may take a little bit longer depending on the original function.
After graphing f′, you may use all the other graphing functions on the calculator (intersect, zero, and value).
dxdy is the rate of change of y with respect to x. That is, dxdy tells us how much y changes in response to a change in x.
If y=f(x), then dxdy=f′(x).