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6 Nov 2019
Sketch the graph of a function y = f(x) that satisfies the hypotheses of the Mean Value Theorem on the interval [0, 6] and has the following properties additional properties: (i) f(0) = 5, (ii) f(6) = -3, (iii) there are at least two points between 0 and 6 where f'(x) = 0. Make the x-axis at least 6 inches long. In the graph you drew in (a), label all the points on the x-axis where the conclusion of the Mean Value Theorem is satisfied. The conclusion of the Mean Value Theorem interpreted geometrically says there is at least one pair of lines that arc parallel. In the figure you drew in (a), draw one such pair of lines. Label each line with the part of the conclusion of the Mean Value Theorem applicable to that line. If the independent variable x in the function y = f(x) in the graph you drew in (a) is time and the dependent variable y is position, then the function y = f(x) describes the motion of an object along a line. In this case, what does the Mean Value Theorem say about the motion of the object? Show transcribed image text
Sketch the graph of a function y = f(x) that satisfies the hypotheses of the Mean Value Theorem on the interval [0, 6] and has the following properties additional properties: (i) f(0) = 5, (ii) f(6) = -3, (iii) there are at least two points between 0 and 6 where f'(x) = 0. Make the x-axis at least 6 inches long. In the graph you drew in (a), label all the points on the x-axis where the conclusion of the Mean Value Theorem is satisfied. The conclusion of the Mean Value Theorem interpreted geometrically says there is at least one pair of lines that arc parallel. In the figure you drew in (a), draw one such pair of lines. Label each line with the part of the conclusion of the Mean Value Theorem applicable to that line. If the independent variable x in the function y = f(x) in the graph you drew in (a) is time and the dependent variable y is position, then the function y = f(x) describes the motion of an object along a line. In this case, what does the Mean Value Theorem say about the motion of the object?
Show transcribed image text Patrina SchowalterLv2
21 Jul 2019