Programm on Mathematica please. Thanks for the future help. In text : Consider the quartic f(x)=26-6 x-(14 x^2)/3+ (x^3)/2+x^4/6, defined on the interval [-7, 7]. Fix a point on the graph. 1. Explore the locus of the midpoints of chords with one endpoint being the given, fixed point, and the second another point on the graph, in the given interval. For practical purposes, for the creation of chords, consider a point moving across the given interval at a step of 0.25. Represent the midpoints in red, along with the graph of the function. 2. Use Manipulate[] to explore what happens when you move the fixed point. For practical purposes, explore a set of points in the domain of the function taken at a step of 0.25. Along the graph of the function and the set of midpoints, represent the fixed point on the graph in green. 3. From the exploration done in point 2, retain from each value of the fixed point, the midpoint of the chord you considered for 0 as moving point. Represent the graph of the function, and the set of thus created points in purple. PS. If you are curious, check out what happens for the cubic. Just choose a function with three real roots, and see your graphs.

Consider the quartic f(x) = 26-6x - 14x2 + +, defined on the interval (-7, 7). Fix a point on the graph. 1. Explore the locus of the midpoints of chords with one endpoint being the given, fixed point, and the second another point on the graph, in the given interval. For practical purposes, for the creation of chords, consider a point moving across the given interval at a step of 0.25. Represent the midpoints in red, along with the graph of the function. 2. Use Manipulate[] to explore what happens when you move the fixed point. For practical purposes, explore a set of points in the domain of the function taken at a step of 0.25. Along the graph of the function and the set of midpoints, represent the fixed point on the graph in green. 3. From the exploration done in point 2, retain from each value of the fixed point, the midpoint of the chord you considered for 0 as moving point. Represent the graph of the function, and the set of thus created points in purple. PS. If you are curious, check out what happens for the cubic. Just choose a function with three real roots, and see your graphs. Consider the quartic f(x) = 26-6x - 14x2 + +, defined on the interval (-7, 7). Fix a point on the graph. 1. Explore the locus of the midpoints of chords with one endpoint being the given, fixed point, and the second another point on the graph, in the given interval. For practical purposes, for the creation of chords, consider a point moving across the given interval at a step of 0.25. Represent the midpoints in red, along with the graph of the function. 2. Use Manipulate[] to explore what happens when you move the fixed point. For practical purposes, explore a set of points in the domain of the function taken at a step of 0.25. Along the graph of the function and the set of midpoints, represent the fixed point on the graph in green. 3. From the exploration done in point 2, retain from each value of the fixed point, the midpoint of the chord you considered for 0 as moving point. Represent the graph of the function, and the set of thus created points in purple. PS. If you are curious, check out what happens for the cubic. Just choose a function with three real roots, and see your graphs