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Graph showing the relationship between the roots, turning or stationary points and inflection point of a cubic polynomial and its first and second derivatives by CMG Lee. The vertical scale is compressed 1:50 relative to the horizontal scale for ease of viewing.

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Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more!

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<< How do I prove that not all cubic functions has a local minimum and local maximum but always have an inflection point? Is there a formula to prove this? >>; first prove that every cubic has an inflection point an inflection is where the bend(sec...

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Move the blue point on the `x`-axis to change the value of `c`, and observe how the line tangent to the `f`-graph at `x = c` changes. When is the slope of the tangent line greatest? lowest? Can you find (at least) one value for `c` where the tangent line crosses the `f`-graph only once, at its point of tangency? Improve your math knowledge with free questions in "Relations: convert between tables, graphs, mappings and lists of points" and thousands of other math skills.

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A graph which can be embedded in the plane so that vertices correspond to points in the plane and edges correspond to unit-length line segments is called a ``unit-distance graph.'' The question above is equivalent to asking what the chromatic number of unit-distance graphs can be.

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Find the point on the graph of the given function at which the slope of the tangent line is the given slope. f(x)=6x? + 2 + 4x - 8; slope of the tangent line = - 3 The point at which the slope of the tangent line is - 3 is (Simplify your answer.

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