a 52 foot ladder is set against the side of a house so that it reaches 48 feet. If Jevonte grabs the ladder and pulls it 3 feet farther from the house, how far up the side of this house will the ladder reach now​

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.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8