Choose the correct response

f(2) = 9

Step-by-step explanation:

It's give in the question,

Two different functions are,

f(x) = 4x + 1

g(x) = -2x

Then we have to find the output value of function 'f' for the input value x = 2.

By substituting the value of x in the function 'f',

f(2) = 4(2) + 1

     = 9

f(2) = 9

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.