8+(2x+7)=6x whats the property ? help

I am very sorry that I am stealing these points. It is personal and I am VERY sorry it had to be you. I totally understand if you report me for this.

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.

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol