At the point of inflection the of the graphs changes. concavity Consider the diagram below. Along the curve PA the concavity of the graph is Along curve AQ the concavity of the curve is concave down. concave up. Comparison between graphs of and Function: Derived function: The x-values of the turning points are the These x-intercepts, are the turning point x’s of the cubic of the graph of , which is x-intercepts y’ =…. graph, because the values here are 0. y- the parabola on the right. The turning point at i, is the of the point x-value x-value The point of x-value is the x-value of inflection’s of inflection on the cubic graph. the turning point of the graph of y’. At this = 0. This x-intercept and the x-intercept, y’ At this the gradient of the tangent = 0 x-value, of the parabola on the left are the same x-value x-values.
At the point of inflection the concavity of the graphs changes. Consider the diagram below. Along the curve PA the concavity of the graph is concave down. Along curve AQ the concavity of the curve is concave up. Comparison between graphs of and Function: Derived function: The x-values of the turning points are the x-intercepts of the graph of y’ =…. , which is the parabola on the right. The point of inflection’s x-value is the x-value of the turning point of the graph of y’. These x-intercepts, are the turning point x’s of the cubic graph, because the y- values here are 0. The turning point x-value at i, is the x-value of the point of inflection on the cubic graph. At this x-value, the gradient of the tangent = 0 At this x-intercept, y’ = 0. This x-intercept and the x-value of the parabola on the left are the same x-values.
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