Exploring Gradients of Quadratics

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2016-09-14 17:32

Function Calculus Derivative

This example demonstrates how to use GeoGebra to explore the derivative of quadratic functions and its geometric significance. Key math concepts include the definition of derivatives, their geometric meaning (slope of tangents), and properties of quadratic functions. Construction highlights involve commands like Derivative, panelleft1, panelleft2, Textfield, Sequence, If, and objects such as function f and its derivative f', along with text display and sequence generation. Suitable for high school mathematics education to visually enhance understanding of the relationship between derivatives and function graphs, deepening comprehension of calculus concepts.

GeoGebra Commands & Parameters

Derivative(f) → f'
panelleft1(200) → panel1, panel1_a, panel1_b, panel1_c, panel1_d, panel1_s
panelleft2(200) → panel2, panel2_a, panel2_b, panel2_c, panel2_d, panel2_s
Textfield(a) → InputBox1
Textfield(b) → InputBox2
Textfield(c) → InputBox3
Sequence((i, f(i)), i, -4, 4) → intpoints
If(b ≟ 1, x, (b * x)) → f_1
If(a ≟ 1, x^(2), (a * x^(2))) → f_2
If(b ≟ 0, f_2(x) + c, f_2(x) + f_1(x) + c) → g
Sequence((i, f'(i)), i, -4, 4) → gradients
Sequence(Segment[Intersect[Circle[(i, f(i)), 0.5], Line[(i, f(i)), (i + 1, f(i) + f'(i))], 1], Intersect[Circle[(i, f(i)), 0.5], Line[(i, f(i)), (i + 1, f(i) + f'(i))], 2]], i, -4, 4) → chords