It's gonna be ok :) That's the most comforting thing I could hear today, and I thought I'd share it with others who need it too.

thank you <3 i agree. i'm verbally abused a lot in school, so i needed to hear that. <3

Step-by-step explanation:

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.