Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6),A(−8,−6),A, left parenthesis, minus, 8, comma, minus, 6, right parenthesis, comma B(-3,-6)B(−3,−6)B, left parenthesis, minus, 3, comma, minus, 6, right parenthesis, C(-3, -4)C(−3,−4)C, left parenthesis, minus, 3, comma, minus, 4, right parenthesis, and D(-8, -4)D(−8,−4)D, left parenthesis, minus, 8, comma, minus, 4, right parenthesis.
Given these coordinates, what is the length of side ABABA, B of this rectangle?
units

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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step-by-step explanation: