Ralph’s annual income is about $32,000. based on his expenses illustrated in the graph below, roughly how much should ralph expect to pay in taxes this year? a. $1,920 b. $8,000 c. $9,280 d. $11,200

the answer is

d. %11,200

(; < 3

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.