Isaac's grandparents get him a puppy for his thirteenth birthday, and he names the puppy Sparky. Isaac does a good job taking care of Sparky, and she's growing so fast! When Sparky is 2 months old, she weighs 6 pounds. When she is 3 months old, she weighs 8 pounds. In this relationship, x represents Sparky's age (in months), and y represents her weight (in pounds).
Graph two points for this relationship and the line passing through them.

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: