Use the diagram below to find the solution to -3/2 + 2

0.5

Step-by-step explanation:

-3/2 + 2

convert element to fraction: 2=2x2/2

=2x2/2 - 3/2

since denomitors are equal, combine the fractions: a/c +- b/c = a+-b/c

= 2x2-3/2

=1/2

coverted to a decimal: 0.5

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.