Given the function f(x)=x^2+10x+23f(x)=x 2
+10x+23, determine the average rate of change of the function over the interval -9 \ le x \ le 0−9≤x≤0.

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.

12

step-by-step explanation:

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