Long description: temp3

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A graph displays a curved line segment and a right triangle formed by the coordinates (a, a^2), (a+h, (a+h)^2), and the point directly below the second point, illustrating a geometric representation.

Alt text: A graph showing a curve and a secant line segment forming a right triangle, illustrating a concept related to derivatives.

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  • The image displays a two-dimensional Cartesian coordinate system with the horizontal axis labeled as \(x\) and the vertical axis labeled as \(y\).
  • A curve is plotted on the graph, passing through at least two marked points.
  • Two points are marked on the curve: one labeled \(A(a, a^2)\) and another labeled \(B(a+h, a+(a+h)^2)\).
  • A horizontal distance of \(h\) is indicated on the \(x\)-axis between the \(x\)-coordinates of the two points, forming the base of a geometric shape.
  • A vertical line segment connects the \(y\)-coordinate of \(A\) to the \(y\)-coordinate of \(B\).
  • A right-angled triangle is formed by the segment connecting \(A\) to \(B\) (the hypotenuse), the horizontal distance \(h\) along the \(x\)-axis, and the vertical distance connecting the two points projected onto the \(y\)-axis.

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